The most appropiate term is a "child born out of wedlock". There is no other word (at least an appropiate word) that has been designated to a child that was born out of wedlock. The bigger issue here, is making the child feel loved and secure.
How about just calling the child a baby. These terms we label children with have a lot to do with their lack of self esteem later in life. They get enough from their peers, they don't need it from their parents etc.
How about calling them a human? We are all unique in our own way. Just love the child. That's all that matters. Labels are awful when it comes to people. It's bad for self-esteem and is a form of profiling much like racial profiling. It's wrong!
You can call him/her "my Baby" or "my gift from God" The term NecroParade used, is just outright mean. True, that is what the innocent little babies use to be called, but think of how that affects the little ones esteem, as someone already brought out. So rather than being so negative, be more positive, and say this is "my baby"!!!!!