My favorite is the Martini action. Well maybe, except for the Sharps, Ruger, or Winchester drop-blocks. And then there is the rolling block which I really like and have several in various calibers, and the Trap-door Springfields and Sniders. Of course, I don't want to leave out my NEF and H&R break actions or the T/C Encores, or maybe my ol' Remington M41 and 510 .22 rim fire bolt action and the Flobert parlour rifle. There is of course also my Lee Enfield No.8Mk1, and No2Mk1 single shot rifles and my Marlin 2000, both of which will shot 5 shots into a dime-size group at 100 yards.
Hell, I guess I never found a single shot rifle I didn't like! As with your kids, do you really have a favorite?