I’ve found the easiest way (and safest!) is to always put single-quotes around the path. That is, of course, unless you have single quotes in the file name. Ack!
do shell script cp '~/Library/.StickiesDatabase' '/Volumes/30 GB Firewire HD/.StickiesDatabase
Well, best thing is to check whatever path you put in, to make sure it is has no quotes and quote it, or escape quotes, spaces, etc if it does. I generally started leaving out spaces and quotes, slashes, etc a few years ago anyway, so that anything I did on my Mac would be cross-platform compatible. Especially important if working on websites. I use alpha-numerics, dots, dashes, and underscores. Oh well.