It seems to me there are two separate things going on here. First, how to use a bi-color LED with the switch machine/controller instead of two separate LEDs. Second, how to use a single push-button instead of two. I'll tackle the LED issue first, since that seems to be the focus of late. I'm sure there are other ways to do this, but this is the first thing that popped into my head.
In place of the LEDs in use in the current controller design you could use a pair of opto-couplers. Then use the switching action of the OCs to turn on and off the anodes of a 3 leg bi-color LED. This is quick and dirty, and may need refinement, but something like this:
You can likely find an Opto with two in one dip package, I just don't have one I could find in the program I use for schematics. I also didn't have a bi-color LED, only a tri-color, so ignore the blue LED leg.
As for the single button, the first question is, does it have to be momentary as the original controller is? I'm guessing that it does, as the LEDs in the controller would not light if the button is held down, and in the schematic posted above by stan, there doesn't appear to be anything to keep the motor from running. Not really sure what's in the guts here. If you can leave the button pushed, than any push-on/push-off double throw button should do the trick. If you need only a momentary contact on the other hand, there are a couple solutions that come to mind. The simplest one as far as easiest to put together for someone that doesn't want to scratch build something at the component level would be to use a timer-relay module from the auction site and perhaps a second relay module along side to direct the power in the right way. This would also need a DC power source for the modules.
One could get the same job done in various ways with discrete components, whether using relays, transistors a flip-flop, or even a micro-controller. each has advantages and disadvantages in complexity and cost. My opinion is, if you only have one or two switches that need such a controller, the pre made module approach is easiest, though it will set you back $15-20 per switch. If you have many switches, the Micro-controller is likely the easiest, least expensive solution, costing about $10 plus $10 for every 8 switches.
JGL