Grab a 7486, 74LS86, 74S86, or 74HCT86 and XOR the sync inputs together. You want positive vsync and negative hsync to get negative composite sync. If you have both positive, you can invert the hsync by using one of the spare XOR gates on the '86 to XOR it with "1" (logic high - tie the other input to +5). Tie unused inputs on the '86 to GND or +5. VCC is +5, GND is GND. The output of the two sync inputs XOR'd together is composite sync at TTL compatible levels, which is what almost all arcade monitors want.
I hate to just connect the two sync outputs together. While it often does work, it can eventually destroy the sync outputs resulting in malfunction.