I kind of like to keep up with who's whose with mine too and tho it's difficult to keep up with the dads, I have managed to keep up with what child belongs to what mother this way...
I basically am running a Twin Peaks village. Everyone in the village gets renamed with the name of a character from Twin Peaks, and when children are born, I give the child a name that's either from that family on Twin Peaks or somehow related. i.e., the famous Laura Palmer on the show was the daughter of Leland and Sarah... so naturally the first girl born to my villagers named Leland and Sarah got renamed Laura.

I'm more relating it to the mothers since there are so many different combinations of dads on my island, but sometimes still an "appropriate" pair per Twin Peaks gets together.
After several kids, when I started running out of family names I would just pick something somewhat related to those characters - such as should Leland and Sarah have a boy next time, I'll just name it Bobby (Laura's boyfriend on the show).
It's working for me to keep up with the moms & kids and who's basically related, though now at 26 villagers I have sort of lost track of who the dads are most of the time (although Leland is impregnating the entire village lately so that's easy, heh!).
And you could certainly use this with many different shows or movies even, tho probably best to choose a set of characters from a TV show or movie that has lots of characters and lots of families to choose from. Soap operas would probably work really well with this method!