Is there a proper way to add alternate covers? Or should I just list as a different release?

If the only difference is album art, you can upload it in images as well and it'll show up in the bottom-right corner of this page under "related images."

You can make a separate release for it as well; I typically do that if there's a reason why it was sold that way (e.g. : member-specific album cover, different versions based on city, live edition vs webshop edition, etc).

@jarvi To expand on @Seraphim's comment:

If the alternate jackets were included in the same release (e.g. a reversible jacket) then you can just upload them as additional images on this release. Otherwise, they should be entered in the database as a separate release.

I googled 実録歌謡大全 第弌集 and it appears to me that the versions were sold separately, so they should be listed as separate releases in this case.