jamaldog87: be careful of using those cor-bons in that old Beretta. The Model 34 is a classic, but a very old classic and cor-bon ammo is higher pressure and may damage the piece.
Can the 380 handle a coyote - yes, if you are close enough.
I have not hunted with a laser sight but considering the rudimentary sights on that Model 34, the laser sight might not be a bad idea - at least you know where your bullet will hit.
I don't know if laser sights are legal to hunt with where you are located so you should best check to make sure you stay out of trouble.
Yes, I have hunted with the smaller pocket pistols and have hunted with the 380. I wouldn't exactly call it hunting, being out in the forest (jungle, actually) with a 380 with a couple of extra magazines and a box of ammo, shootin' at anything that moved and was edible; but small monkeys, kotamundi, any number of turkey buzzard, a whole bunch of large snakes, tons of land crabs, a number of turtles and even a few small crocs were taken with the 380.
Back then I was using a Walther and handlocading my 380s with a cast 95 gn swc that worked well in the pistol. Mikey.