I don't mean by breeding.
Yes, it can be. chances are 1/8192 in gen 5 and below. Chances are 1/4096 in XY. So you can soft reset till you get one.
Hope I helped!
Its possible to get a shiny Pokemon revived from a fossil but the chances are 1/8192. (On BW/B2W2) On Pokemon X/Y the chances are 1/4096.