Some perhaps appropriate, some perhaps not:

THE MONKEES:   "Daddy's Song" (and definitely NOT their "Mommy and Daddy")
THE DICTATORS:   "Baby, Let's Twist"
THE RAMONES:   "Babysitter"
BIG STAR:   "When My Baby's Beside Me"
THE BAY CITY ROLLERS:   "Mama Li"
PHIL SEYMOUR:   "Baby It's You"
FIRE:   "Father's Name Was Dad"
HOLLY & THE ITALIANS:   "Baby Gets It All"
TAMMY & THE LORDS OF MISRULE:   "What Baby Wants"
JOHN HIATT:   "Your Dad Did"
WAYLON JENNINGS:   "Only Daddy That'll Walk The Line" (also covered by The 
Skeletons)
KIRSTY MacCOLL:   "You Just Haven't Earned It Yet Baby"
THE BEACH BOYS:   "Good To My Baby"
THE BEACH BOYS:   "Kiss Me Baby"
THE HOLLIES:   "Baby, That's All"