If you're a ClubFoo member, you can sell a FooPet back to the Adoption Center at any time. Go to your profile tab, and click on the pet you want to sell. Then click "Sell Pet". The price of the pet is autogenerated based on your pet's stats.
Alternatively, as a ClubFoo member, you can sell a FooPet to another member, with either a private link or a general "first come first served" sale.
You cannot sell your last FooPet - you must own at least one pet. Remember that Baby FooPets must be weaned before you can sell them.