You know, there are several songs that have been/could be suggested and many of them would work quite well; folks can also discuss or argue the correctness, rightness, bestest (I love that word) or uselessness of any, or all of them; however, as a performer of family material at pubs, libraries and Celtic festivals on a regular basis, I can say without equivocation that there is one song that bridges all and never fails to delight the children AND the adults -
"The Unicorn Song."

Sure, it was written by a Jewish guy from New York, but it has been a part of the "Irish community" since the Irish Rovers released it to a world-wide audience back in the sixties. When you add in the
"hand signs" that go along with the song - you can't miss.
Good luck,.............mwh