What you need is a toggle flip-flop. Take a 74xx74 dual D-flip flop. Connect the Q-bar output to the D input. Tie Preset-bar and Clear-bar high. Run your input to the clock. On each rising edge of the clock, the output will go to the opposite state. It will toggle. For the other flip-flop in the package, tie all the inputs high.
I think he will want to debounce the switch. the circuit will work great with clean input but contact bounce will make it a coin toss as to what the next state is.