Cass ... There are a bunch of really old ones such as Let Me Call You Sweetheart; Peg of My Heart, Bye, Bye Blackbird etc. and I also do You are my Sunshine/When You're Smiling; Down by the Riverside; He's got the Whole World; Johnny B. Good (go Johnny go)
I will also do songs where they can sing a 'lead line' such as Goody,Goody; King of the Road; (keep away from)Runaround Sue; Teenager in Love; even Elvis' Wonder of You ...
Hope this helps ...