I run into the same issue when playing Robotron 64, when trying to run diagonally (two buttons) and shoot diagonally (two more buttons) at the same time. My button limit seems to be 2 or 3, so I can't play the game too well unless I plug in my PS2 controller and SuperJoy adapter thingy (I forget if I got that from Lik-Sang or Amazon. I got a DDR pad from Lik-Sang, but it was bending pretty bad and my cat tore it up, and as we know Lik-Sang is no more). Only problem with the controller? Project64 whines if I try setting a button to an input that already exists. That's a problem because the right stick is always slightly tilted, so Project64 keeps thinking I'm setting a key to that. So not only can I not use the right stick for shooting, but I can't really set to use the other buttons either because it keeps thinking I want to use the right stick.
Considering the PS2 controller has two L buttons and two R buttons, I should just learn to substitute A for R1, B for L1, R for R2, and L for L2. That way the whole face of buttons can substitute for the C buttons and I wouldn't have this problem anymore. Or I could, you know, buy another PS2 controller.
I'd buy a SNES controller and adapter for when I'm more often playing SNES games, but that just looks too expensive.