I was thinking about ways that other sites keep the breeding population down, and a release reward seems to be pretty effective. Please excuse me if this has already been suggested.

On Lioden, I imagine it would be a randomized small payout of 10-50SB for chasing any lion under 3 years. The age limit prevents players from impressing NCLs purely for the sake of chasing them to get SB, but also allows the player to have a look at the lion's grown up form before making a decision.

While it doesn't decrease the breeding rate, it would essentially put a price floor on cubs and adolescents and increase the incentive to chase them instead of trying to hold out for a buyer.

It probably won't increase the breeding rate either. Since there's no cost for junk breeding to your own male right now, I assume that players are already breeding at the maximum rate, and then trying to sell the cubs, which means it can't go up even if there's more incentive to breed.

On the whole, I expect the feature to do more good for the economy than harm.

Modification: Breeding Fee
In order to combat inflation, a breeding fee paid by the owner of the female to the site can be implemented. If the breeding fee is greater than the average SB gain from chasing a litter of cubs, no inflation will occur. If the breeding fee is greater, deflation will occur.

In addition, a breeding fee will discourage users from junk breeding, decreasing the total number of cubs born, and encourage players to chase their own cubs instead of trying to sell them, in order to make back the cost of the breeding.