Thanks SavannahLion. Sounds complicated 
I'm just going to connect saturn joypads to XBOX360/XBOX controllers.. with 15pin joyport cables.
I think I understand. OK, so you're planning on gutting the controller. I like doing
less destructive ways, but it's a far more complex project and one has to start somewhere, right.

I don't have direct experience with Saturn controllers, but I understand the control chip is really a dual multiplexer, turning the parallel button presses into a serial data stream. Looking for PCB photos and schematics, I did locate someone
who did what I'm about to describe and even marks soldering points.
Look for the small IC and remove it. Then wire away. I was thinking you should use XORs with an AND. That might not be right since I tend to think in terms of always needing a high signal. Looks like it would be a two
XNOR gates and a OR gate. Good luck finding that combination. You can construct your own using several NAND gates, but that would eat a lot of IC's. You can try PBJ's suggestion, go with IC's, or even convince someone to assemble a small circuit board with the behavior you want.
Another option would be to buy a small switch, drill a hole somewhere in the controller and wire it up using that. I wouldn't do that though. I don't really like modifying controllers like that.