I'm ripping my whole CDs collection and want to add APEv2 tags to all the files, everything goes fine except that some albums consist of more than one CD, and I don't know what APEv2 tag should I use to store the disc number information. I took a look at the APEv2 tags specification, and there doesn't seem to be any standarised tag to store such an information. So what should I do? Use the COMMENT tag?

Foobar2000's default title formatting strings (at least up to 0.7.4 version) used 'disc' tag for that purpose, AFAIK.

That's not a standarization of any kind, but perhaps it may help you.

Currently I have fb2k v0.7.5, and I don't see a DISC tag in its Mass Tagger... Of course I can force adding a tag like DISC = 1, but will it be ok to add a tag like DISC = copper disc? Can I use string values or integer numbers only?

What I am using, and from what I know others too, is DISC for number of the disc and DISCNAME for string denomination of that disc if any of course.

APEv2 does not use standard fields, although a few obvious ones like TITLE, ARTIST and ALBUM are used by the common audio players we see today.
As far as I know, in really flexible players like FB2k, you can misspell ALBUM as ABLUM, code title formatting to accept the change, and your ALBUM information will still display as you want them to.
So, DISC is a good field to use.