It is pretty straightforward to JAMMA-tize DECO stacks. As Mitsu likely encountered though, the video pinouts shown in documentation are backwards.
For the SLIM stack, I mostly used spare Molex connectors I had on-hand, and a 50p IDE-style cable for control connections.
For the PHAT stack it gets a little more complex. Couldn't find a connector even close to the one used for power, and no QD would fit on those posts, being so close together. So I simply tacked on a connector I had both male and female on-hand (later-style Nintendo video jumper cable) onto the bottom pins of the stock connector housing. Then simply follow the same config as the SLIM for the rest of the connections.
Of course, the PHAT stacks don't have on-board audio amplification, so I used a JAMMA fingerboard designed with the option for one.