You'll have to protect the teensy if it can't handle 5v.
Inputs on JAMMA boards are active low. This means that they're pulled high from the board side. This is usually accomplished with a resistor array as a pull up, so the voltage will be close to 5V.
When you press a button, the input is grounded so this is what you have to accomplish.
There are level shifters that are also buffer drivers so they can easily sink the current from the board. I think TI has what you want... From memory, you can accomplish this with the 74lv16(something)245. Input a low from the teensy and the IC will pull down the JAMMA input, simulating a press.