I just adopted a bloodred cadogre today for a friend who can't adopt yet. When I went to the pet resort, I did not see my cadogre's name in the list of available pets to put in; however, the pet shows up at the training center. I want to put the cadogre in the resort until my friend can adopt (receive) pets.

The original owner might have stuck it in the resort, I wouldn't worry about it too much. c:

I was thinking that might be the case, but the happiness bar is at zero. Shouldn't the pet be happy (like my other two in the resort)?

Technically, yes. That should be at least partially full if they're in the resort, having a minion can also effect that.

I'll try waiting for 2 weeks. Maybe being in the adoption center made it unhappy?

There's a good chance that the original owner made the pet then stuck it immediately in the resort then the adoption center right after that. But yeah, I'd wait and see if the happiness goes up and if the pet pops out of the resort in a few days before getting too concerned.