Natural child is probably the least potentially offensive, which makes it a favourite with family historians, but it is also rather odd, implying that children with married parents are unnatural.
Born outside wedlock is cumbersome and sounds archaic and coy. Born outside marriage is not much improvement.
Illegitimate is precise and formal, but carries an undertone of illegality, seeming to imply such a child has no right to exist.
On the whole I think I prefer bastard, which may still be used as a term of mild abuse, but has the capacity to be reclaimed.