Well none of these ideas on their own will really fix the issue and ill point out why down below. A combination is clearly the best way to go if the issue is to be fixed and slight adjustments will need to probably be made.

1) Breeding charges. This idea alone is probably in need of being implemented but it will present a different issue. The market and tree will suddenly be flooded with pets that can't breed and players will be angry about it. However, this idea does make it so players actually need to switch out their animals and not just breed them once a week or whatever. Switching them out wont take time because you can just breed the pets you have already bread and get rid of the parents. In the end, the over breeding will simply continue.

2) Stable Limits. Stable limits won't have much of an effect on the over breeding issue. Its mostly an idea that will try and encourage people but if its 50 stables over 10 villagers, that's 500 stables. You want to encourage players to breed their favorite pets but those who just breed for profit or fun can still breed all the pets but slightly slower. While this would technically reduce the over breeding issue, I don't believe it would reduce it enough to have the effect you are looking for. At least not on its own.

3) Account-wide breeding limits. This is probably the best of the three and is surly to have the most impact on controlling breeding amount. It would encourage players to trade and try to get more breeding charges per day for sure. However, this may cause players to find the more rare animals impossible to get. It will possibly slow down the AH a bit too much in the end.

4) Breeding potion overhaul. Frankly, I love this idea. It gives the game a bit more depth which is something I feel it needs. However, I feel it would be extremely tedious to come up with like 100 breeding potions every time you want to mass breed your animals. It would certainly stop over breeding for sure and change the AH as little as possible AND give all rarities of animals more value... probably.

As I stated above, I feel a combination of the ideas is the best way to go. Here is my idea using all 4 of the ideas posted.
Limit the animal stables to 50. Set max breeding charges per 8 hours to 200. Give animals breeding charges as suggested BUT don't allow animals with no breeding charges to be posted on the tree or sold in the market. Let them be sold to the NPC for fc depending on rarity or consider having a pet adopt section which will be flooded with non breedable animals. Revamp the breeding potion as suggested but allow each potion to be used 5-10 times instead of one. This way, its a bit less tedious to breed and still gives that connection with alchemist and AH.
To make sure everyone's happy, maybe keep the current version of the breeding potion but change the name to fit what the potion does. Currently, I feel its name is misleading.

I don't breed. That being said, these constant changes that are made to keep people from making money is what is keeping me from this game. Ho-hum.

i like the potion idea. otherwise, #3 is my favorite. breeding limits are much better than limiting stables, i think.

I really, REALLY hate the breeding potion idea. I would no longer bother with breeding because it would be more trouble than its worth in all honestly

I would however be up for a situation where if breeding charges are implemented you could use a special potion to renew the breeding charges to a certain number. This would make it so that people would be spending more funds on their uncommon and rares and could still give the alchemy connection.

Out of all the ideas, I like the idea of breeding cooldowns most, then breeding limits second. I don't like the idea of limiting stables at all. Cooldowns + the potion idea I mentioned are the most interesting to me.

I also like the 'at the end of its life cycle you can trade it in for some sort of points' idea people post.

But tbh like others said, why not just give us a new use for pets like a point turn in system or whatever. Then no one has to be punished. I mean...The pet rarities are so low ,i mean .5% for a super rare??? That right there is the reason for the over flow of pets. But turning them in for stuff would be better than a rarity change...

Very true Aelys I like your idea a lot! :) Just being limited one way or another just feel disappointing.

uhm no, using a breeding potion to breed is an awful idea. It hard enough to get rare colors as it is. Plus how would we swap their genders???

And I say limit stables, I already work on only my faves and just use my storage. I find it almost crazy how many stables people have...Then again I'm not in to it for profit.

Or 100 bredings per day wouldn't bother me either tbh.

And charges ahaha...No...Please no...I don't want to see a million animal duds on market. That would be even worse.

Trying to collect at least 1 of every animal is one of the few reasons that I still login regularly to play. I don't participate in the economy at all; I don't buy or sell anything since the 'tax' was introduced.

I feel that when people want to 'fix' the economy, they usually go about it the wrong way. They start looking for ways to limit people playing the game the way they like to in order to raise the value for their own stuff.

Instead, while limiting what comes into the economy is helpful, what is more helpful is looking for ways to take items OUT of the game and economy.

One idea I had, and it has been slightly touched upon here, is a shop/kennel/whatever you want. You take your pets and turn them in for points. One thing I would LOVE to see in the shop would be, potentially unbreedable to help them retain value, alternative colors for pets.

Here is what I mean. The Unis have White, Appaloosa and Stardust (that I have bred so far)

In this shop there would be variations on the appaloosa and up colorations (most common colors I don't think would need variations). For the appaloosa, it could be same pattern but different coat colors, as well as different appaloosa patternings in different colors.

This would give people reason to actually turn in animals and if you had to turn in specific animals, like say for every appaloosa coloration you had to turn in 50 white unis, and ONLY 50 white unis would work, this would mean people would be getting those off the market. To keep things fresh, you could cycle the colorations in and out of the store, as well as add new ones over time.

In conjunction to this, add some of the other ideas to get pets out of the system and give them a use other than a rather pitiful sellback price.

Implementing these ideas in conjunction with perhaps number 2 or 3 (definitely not 1 as people have said, this would only shift the glut from common breedable pets to common unbreedable pets that are useless) I think would do much more to help the pet economy than trying to make sure that those with huge breeding farms can no longer work.

I hope that the breeding %s for colourations do not change. This is one of the main features of this game that I have been very impressed by, because it does not devalue the rarer colours of pets as people climb the ranks to get the super rares. Getting the rares & super rare colourations as they are, I think, is great. It takes time, yes, but you get more kids each time and have more chances to get that. I like that it;s a long process that isn't easy.
Now, as for limiting stables or breedings per account... I think that anyone who sets up large farms is already taxed by stable-costs/repairs as well as the time it takes to do so.
Not to mention since we have the 10 worker limit, how are people going to breed all the pets they need to complete their menagerie if we limit stables on top of the costs of making and maintaining those stables. It will take ages and will make all of the super-rares completely out of reach for most people because their prices will skyrocket.
I think increasing pet sell-back prices would help to get them off the site.
Breeding charges would take some getting used to, but I think they sound reasonable. What would happen to the pet once it loses it's charges? Would it still be able to be put in your menagerie without any breeding charges left? Would it disappear?
I also think that offering some sort of 'cash in x amount of this pet' in exchange for recharging breeding charges would be a brilliant idea! This could be set up like the alchemist shop, but at the pet shop? The shop owner would have an option to accept pets and a fee, in exchange for recharging your chosen pet's charges.
Breeding potions sound like a great idea, too! BUT they would need to be able to be crafted in each village. They could be like houses, you can only use this town's potion when you reside in that town to help your pets breed. That way we can still raise pets from other towns, and QP's breeding potion should be renamed to Gender Potion, for sure.
I know that you guys want to encourage us to work with others in the community, but I think a fair chunk of us like to spend our limited gaming time in this game only using the marketplace and sellback, and I think that is perfectly viable and reasonable, so I really would like to see more ways of turning things into the site in exchange for small payouts/rewards, and am happy to see that Questing is helping there, too.
I really think that the pets sellback should be increased and that would help a lot. There are a ton of easy features and activities that can be added to the site to become money-sinks, and I think the limited population is exaggerating the amount of deflation to items and desire for a lot of these items too. (Most people only need 1 of each gender of each pet, that's why all the uncommons and rares are sinking in value. We don't have enough people to sell these items to.)

All in all, I would like to have a grace period for whichever changes you guys choose in the end! If you will be cutting down on stable limits, I would like time to remove my pets/stables without losing them, is all.
Thanks for your time!