When Belle was born, I felt like I needed some that were more specific for non-mobile infants and the following are what I came up with.
Rock and Roll (the baby!)
tune: Raffi's Shake the Sillies Out
You gotta rock, rock, rock until you roll
Rock, rock, rock until you roll,
Rock, rock rock until you roll
Rock till you roll all the way over!
I sang this while rocking Belle's body from side to side and then at the end rolling her over unto her stomach. She thought this was great fun and then enjoyed being able hold her arms out to prevent me from rolling her over (and who says babies don't have other ways than crying to communicate!) Of course, Willem wanted to join in on this game so I'd take turns. First with the baby, and then with the 2 yr old!
Tickle, tickle, tickle tickle tickle
tickle tickle tickle tickle tick
Tickle all the way up to the neck
Tickle all the way down to the hips
Tickle up here,
Tickle down there
As suggested by the lyrics, I tickle all over and then specific parts. My favorite is tickling the feet on "tickle down there" and making sure I sing with a deep voice as I do so.