A couple of questions come to mind. (Not sure if they are relevant just information I would want to know if I was preparing the return.)

Does he live with her and the child.?

What is the custody situation (from a legal standpoint)?

Is he OK with having the payments to him reported to the IRS (As surely someday they will get around to matching the 2441 information of payee's (Name, SSN Amount ) to the see if the payee has properly reported the income.

Probably a couple of others but those just popped into my head.

If the answers are 1. no and 3. yes I would think you could claim it on the 2441, but probably not for any time that a custody agreement could be interpreted as the child being with him as part of the custody agreement. Again, quick off the top thoughts.