Abilities are the color of the source that created it, so a triggered ability from Constricting Sliver will be whatever color that permanent is. If Ghostflame Sliver removes its colors by making it colorless, the ability will equally be colorless and can target Animar.
I'd also like to point out that the title wasn't chosen particularily optimal, as the question has little to do with how Animar specifically works. Just saying...
June 12, 2017 11:05 a.m.
It's also worth noting that if they have out Constricting Sliver and then play Gemhide Sliver they can exile Animar, Soul of Elements because even though the ability is granted by the white Constricting Sliver, the source will be the green Gemhide Sliver.