First off, there are better, cheaper ways to add other functions to mame... I'd suggest you'd look into them first. Probably one of the best old-school hacks is to hot-glue a bladed microswitch onto your coin door on the inside so that the plastic tab on the coin return switch trips it... boom, you've got inputs for the coin insertion that don't actually require you to insert coins. Also see shift/shazam keys on the more popular keyboard encoders.
With that out of the way, this is just a guess, but it sounds like the stream deck is using some sort of simulated (software-based) keyboard input. Mame just doesn't cooperate with that. If you can get the deck, via third party software, to use joystick buttons instead, mame WILL accept simulated joysticks.