How much is it to put an old cat asleep?

Ask your vet. If you don't have one you can Google ones in your area and check their reviews.

The SPCA of Wake county is for adoptions. They don't put cats to sleep. Sorry for your loss

Depends on the vet

Does this center put dogs down?

don’t know about cats, but $75 for a dog at Brookhaven Animal Clinic off 401 toward Fuquay