The connectors are .187"
(3/16ths) disconnects, the originals are, I think, Molex brand insulated connectors...just in case you wanted it fully authentic-like. </nerd>
As best I can tell, that size is used throughout the cabinet, with the exception of the speaker connections and test/service buttons which are .110", and I think the fuse/power switch connections which might be .250". 3/16" is the standard size for non-Japanese arcade pushbuttons, so it's always good to have a stock of replacement connectors. A good old-fashioned automotive-use wire stripping hand tool typically has spots for crimping these. It pains me to no end that it seems impossible to find a good one anymore, all the ones I've seen are flimsy pieces of junk, so I'm stuck with a grimey old one that probably predates me by a bit.
As for your other problem... I take it you mean the LED credit counter? That's a custom SNK board, you're not going to find them new.
(Until I start making my own, which is something on my to-do list) If the rest of the board is working correctly and it's just the LED display, a suitable replacement shouldn't be hard to find and install, assuming you know which end of the soldering iron to hold and all that.
If not, there's always eBay, they seem to show up there pretty consistently.
(Though sometimes terribly overpriced.)