I usually coordinate all the event tickets for our group. I'm connected with everyone via the friend system. This year, one member is bringing his 9-year-old daughter along on Sunday. He has a child wristband and a Sunday badge for her already. Is it possible for me to get tickets for her? She doesn't have an email address.

Just get "another ticket for me" and use that for her?

I would suggest using the 'buy another ticket for myself' option that is available on the specific event screen. 

There is one event that I am not planning to attend with them, so getting a ticket for me would block my schedule. I suppose I'll just have the friend submit his own wishlist for these events.