Banana Boat Song never fails. Everyone likes the "Day-O" bit.
Rock my Soul (in the Bosum of Abraham) is good for easy part singing. Done the way Pete Seeger did it. ie. One group sings "Rock my Soul" and another sings "So High I can't get over it".
Also some of the well-known rounds work even with non-singers.
"Sweetly Sings the Donkey". "Frere Jacques". "Row, Row, Row Your Boat".
Cheers, Joy