You could modify the counter circuit on this website to have two digits (instructions are on the page) and then set up a system of AND gates to trigger a reset when the output of the display is showing 60, but that seems like a lot of work. Program a PIC to count to 60 and reset.
Yhep, without a micro controller this would be a lot of wiring. You'd need a bunch of 4017's and then you'd need to rig a series of AND gates like Aaron said to trigger them correctly. I've done this with two 4017's to count to 16 and even that was kinda long to do.