If the overload isn't good enough, I'll point you to "The Mind's Eye" where they had the weapon set on autofire. If a cell phone half the size of that phaser today is almost as good as a computer, I think in a couple hundred years a phaser would have a delay setting to auto fire.
Though really the concept that death core ican only be damaged by phaser fire somehow and not explosions is a cop out at best. The thing was so unstable that a hand weapon damaging it caused the whole ship to explode. So the 24th century equivalent to a hand grenade which has far more destructive yield(see the episode where Ro and Geordi become ghosts, forgot the name off hand) than a plain phaser bast, should do the job.
There's really no getting around it. The way they killed off Data was clumsy and just made the characters look dumb.