After the party is over you can give them cupcakes.
Hmm, must be a friendship level thing then.The funny thing was, she wasn't. Apollo (who was the host), Gabi, and Sherb were. What's more, I was actually able to give Apollo a cupcake and got a SECOND birthday-themed item from him.
I gave away a few other cupcakes (which IIRC, included Gabi and Sherb) and only got regular items O_O