In the only battle with Trolls mentioned in the First Age, the Nirnaeth, the trolls turn up after sunset.
Trolls of course would have been in other battles, but again, when the sun was down, or blocked out (Morgoth likes his dark fumes).
Interesting question about the Silmarils...in the early tellings of the Making of the Sun and Moon, Laurellin's last outporings of light (just Laurellin's afaik) are distrubingly huge and bright, and when the last furit is taken, it is almost unbearably hot and bright
to the Valar, who could handle lots of heat and brightness. Some of them are scared by what they've done in making it!
So maybe it was just this extra-ordinary deiing light that turned Trolls to stone. Maybe not. At the least, a Silmaril would have terrified them.
Actually, if a Silmarill could do it, maybe Galdariel's Phial could as well. Who knows? (Actually, if the Phial was "easy" to produce (so there could be many) it would indicate that it, and maybe Silmarills, couldn't petrify Trolls, as otherwise all the armies fighting trolls would have one. But then again, maybe the Phial was a one-time thing. Who knows?!)