It would help with details (pictures) about the coin slots - i.e. if there is any bulb holder and what kind if so etc.
In general LED's must stay under their maximum current, so if you didn't have any proper resistor they will for sure burn. Go for LED bulbs with resistor built in and then power them with the correct voltage. Usually 5 or 12V. Anyone selling pinball parts will have them.
If you have game cabinet you probably already have 12V somewhere regardless if it is a MAME PC or original arcade game PCB. Perhaps if it is an RPI you only have 5V, but there are LED bulbs with that voltage rating as well.