Well, I suppose that's already happened, in a sense. Back in the day a group called The Four Preps wrote a song I could claim as my own. They dedicated it to Fidel Castro and it was called, "If we had to do it all over again, we'd do it all over you."
Hmmm...interestingly, even though they aren't neccesarily my FAVORITE bands I think I'd want it to be something like Daughtry or Alter Bridge's music. Something like Life After You by Chris Duaghtry. Oh!! Or a song like Iris by the Goo Goo Dolls or The Man Who Can't Be Moved by The Script...I'd love that. Great question, btw.
Lay Lady Lay by Bob Dylan Except when pregnant, each time my husband kept following me around the house with his guitar singing "She's Having My Baby" and I tried to grab his guitar and hit him with it ha ha-fun memories.
Somebody did write a song for me and sang it to me for the first time at our wedding. I wish if somebody else wrote a song for me it would be more sincere than my ex-husband's song! Maybe - just a song about my chihuahua or my car? Or just the truth - Baby, it ain't happening! :)
Make it special, have a name for him/her. It doesn't need to be romantic, you could write about something weird that happened to you, or you could write about something funny that happened to you guys, the possibilities are endless. I'm a song writer and if you need any help, just ask me.