I cannot remove the battery compartment cover

Are you saying there is no slot into which you can insert a coin and twist?

I have a similar problem. Trying to use a coin to open the battery cover in the magic trackpad, but it won't budge. Any suggestions?

If you have a long handled, thick ended screwdriver, that may be better as you will achieve greater leverage with that. And if you get it off, check carefully to see if the reason it stuck was because the battery had leaked. Were that the case, you will need to thoroughly clean the inside of the compartment.