What is the goal here ? Build equity for the child ? Get him (or her?) out of the house ? Is child employed and has income ? Can child qualify for a mortgage ?
Ideally the child owns the property and the mortgage. You help with downpayment, via a gift. No taxes payable on gifts. Just wire the money, or give him/her a cheque. You could co-qualify for the mortgage, if child cannot by him/herself. Ideally the mortgage is not in your name though.
Do you want to be a landlord ? Are you willing to evict child if rent is unpaid, as that is what you must do on occasion as a landlord. As such, assess this likelihood.
The bigger picture in your post is missing and would help for better insight by forum members.