It could have been a planned bastard child, there are quite a few independent women these days, who might want a child without getting married. Former Canadian PM, Pierre Elliot Trudeau, had fathered the daughter of Deborah Coyne, in such an arrangement (they will never stay together, she wanted a child of with his genes which she will raise).

Don't see how he could have hid it from the other Avengers...but it's possible that he did it before he realise how dangerous the superhero life would be and cut off contact. It's also possible that he did it BEFORE Afghanistan, when he suspect that he might never marry or died young, and here's a very flattering proposal from a woman who he knows will be a good mother.