"Archivable" or "archiveable"

Archivable is correct. -e more often than not drops off when adding -able (it varies a lot, mostly based on whether the word looks better with or without the e; I wouldn't say this is a case that greatly calls for keeping it, and the Google stats tend to indicate others agree).

It is archivable, in the same way from cite you get citable.

There are some differences between British English and American English. In British English, such adjectives (derived from a verb ending in -e) are preferred when they end with -eable; in American English, the preferred form ends in -able (the -e is removed from the verb).
The dictionary I have (the NOAD) doesn't report the word archivable, but it reports citable as derivative of cite, and archival as derivative of archive.

The best reference point I can think of is "livable." I found this post because I had the same question about an interface I wanted to name "IArchivable." Looks to me like--regardless of how we got there, the consensus (on this side of the pond) is "archivable." So, that's what I'll be using!^)