My candidate for Vicki's father is Paul Stoddard. From what was aired, I think the resolution would have been that Paul fathered Vicki in a torrid "affair" (that could have actually bordered on rape) with Betty Hanscomb. I think that Liz must have had some emotional tie to Betty--perhaps it was as simple as they were around the same age and played together as little girls--and felt obligated to help Betty conceal the pregnancy and when the time came, find a home for the child.
I have to confess, though, that I've always liked the theory that Liz was really Vicki's mother. It comes out really strongly as a subtext of many scenes the two had together.
G.