Near as I could figure it out, I should have a separate GameCenter account. I hope to get my iPhone next week, so I went ahead and got a Gmail address so when I get my iPhone, I'll use that Gmail address to set up my GameCenter account and my son will continue to use our home email. He's 8, so it's good for us to see what sorts of emails he's getting. Looks like he could play on my iPhone when I get it if I log out of my GameCenter account and log him in. Sounds a little awkward but do-able. Is that about how it works for others? Thanks for responding, Katie! Playing as a team and using the advice from this Wiki, my son and I have built up an awesome park for him with a Bloom, Sakura, two Butterflies, an Emerald and another egg in the nursery - so I'll have a job to get my own park looking half as nice as his, but I'm looking forward to trying!