Facebook has made both friend and unfriend commonly used verbs. To begin with, quite a few people objected to this verbing, and quite a few people ranted and raved about it. That didn’t stop either verb from becoming perfectly commonplace and more or less ubiquitously accepted, of course: everyone knows what they mean now, and nobody bats an eyelid at seeing or hearing either these days.
Favourite is quite analogous to friend here: it is a noun (and an adjective) that can easily be verbed in the same kind of context and with the same kind of meaning. Although I can’t think of any specific sites that use both favourite and unfavourite as a verb in this way1 (add to favourites or just fave are more common), there is absolutely nothing to stop you from doing so. Creating a verb (usually a causative one) from a noun or adjective by zero-derivation is exceedingly common in English, and can more or less be done with any noun you want, at any time you want.
The prefix un- can also be productively applied to just about any verb where it makes sense to add a prefix with the meaning:
Denoting the reversal or cancellation of an action or state (ODO)
If you can cool something (= make it cooler), then you can also uncool it (= reverse the action of making it cooler); if you can friend someone (= make them a friend), you can also unfriend them (= reversing the action of making them a friend); and if you can fav(ourit)e something (= make it a favourite), then you can also unfav(ourit)e it (= reverse the action of making it a favourite).
Finally, while no dictionaries apart from Wiktionary have yet picked up on the verbal use of (un)fav(ourit)e, Googling either term yields many thousand hits, which at least shows that you are hardly the first person to use these words.
1 The verbs favourite and unfavourite are in frequent use by developers for and users of Twitter, but on Twitter itself, only favourite is used: when you hover over the star icon in a favourited tweet, the tooltip says undo favourite rather than unfavourite.