How could I get DNA of my child's father who has been dead for 19 years?

Maybe an experienced matrimonial lawyer in your locality knows how to do so. Nowadays it is not hard to obtain DNA from a recently deceased person, since the pathologists will keep and store blood. I don't think this was frequently done 19 years ago but it might have been. Check with the hospital where he died, if he died in hospital. If not, there may have been an autopsy required under State law. In that case, find and check with the pathologist who conducted the autopsy. Good Luck.

Not easy, and perhaps totally unavailable.