I don't know any other way except for a court order and in that case I believe one of the parents is responsible. Why not try the one you can buy at Walgreens? Its like 30$ then you send a check or money order for another 100$ I think and you get the results... don't hold me to this because prices could be wrong.but I know they sell them because I saw them there lol.
Court ordered tests might be...since the court is ordering them...so any type of paternity suit would prompt that
If you go through ors or irs and request child support and open a case they make the father take the paternity test and they usually pay for it . And you can close the case afterwards.
Jerry springer ;)
Lol
Sorry but I don't believee its possible unless you've been raped.