Activable or Activatable?

Well, I don't normally use either. If I had to form the word on the fly, I would probably use activatable. But activable does fit the pattern used for some other verbs.

The suffix -able usually attaches to the bare form of a verb (sometimes with spelling changes, like doubling the last consonant letter or dropping a "silent e"). But for some verbs derived from Latin, the corresponding -able adjective is constructed on a different stem.

As a general class, -ate verbs are derived from Latin, and many of them have corresponding -able adjectives without the -te: separate and separable, estimate and estimable, replicate and replicable.

The specific verb activate seems to not actually be derived from a single Classical Latin word: the Oxford English Dictionary says activate was formed in English from the adjective active and the verb suffix -ate. (However, the entry does mention a "post-classical Latin activare (13th cent. in a British source)").

But if we treat the replicate/replicable pattern as a general rule that can be considered productive for any Latinate -ate verb, regardless of the details of its etymology, then it is valid to form activable from activate.

I would say that any simple rule about the use of -atable vs. -able will probably only describe one possible pattern of usage; the actual usage is kind of messy. With that caveat, here is the advice given in H.W. Fowler's Dictionary of Modern English Usage (first published 1926; re-published 2009):

Verbs with the Latin-derived ending -ate that have established adjectives drop the -ate (demonstrable, abominable, alienable, appreciable, calculable, expiable, execrable, &c.); & nonce-adjectives from such verbs should be similarly formed (accumulable, adulterable, educable, confiscable, saturable, &c.) except when the verb is disyllabic (dictatable, creatable, castratable, crematable, locatable; not dictable &c.

(able, 1, p. 2)

On the other hand, the Google Ngram Viewer (mentioned in a comment) shows a preference for activatable: