By the rules, attacks against regenerating creatures do non-lethal damage. Suffocation is a condition, not an attack in the normal sense, and doesn't do an explicit amount ofdamage, so drowning, strangulation or smothering would work.
Since the unconscious Troll isn't holding his breath, strangulation/suffocation goes to work immediately. His actual hit points drop to zero. If, by some rationale of the DM's, this makes him come conscious, that's okay. He'll try to break out of the stranglehold, because if he doesn't he's dead. That effort, while at zero hit points, will put him to -1, whether he succeeds or not. And again, that's real hit point loss, not from any attack but because of his own efforts while wounded. Now he's in shock and dying, and Regen can't help. He's dead unless he can stabilize.
Need him dead faster? Keep strangling. Do that and he's dead in a round, and stabilization never comes into play.
There's a way around pretty much everything, if you know the rules.