The terms "baby mama" and "baby daddy," it turns out, originated in Jamaica in the 1960's and migrated to the US via song lyrics. Once they were popularized in hip hop lyrics in the late 90's, the terms lost most of their negative connotations. At least to the clueless white people who did the popularizing and who presumably don't have as many actual firsthand experiences with trying to get diaper money from a baby daddy who just bought a new set of rims for his Hyundai.
Meanwhile, the tersm still carry a sting in Jamaica:
On the island, your baby-mother or baby-father is typically someone with whom you are no longer romantically involved. If you called your husband your "baby-father," he might be insulted’Äîthe term suggests biological fatherhood in the absence of any real parenting.Where Do "Baby-Daddies" Come From? [slate]
Previous baby daddy coverage on daddytypes, serious and not.