I'm of the opinion that until someone can make a decent pulse laser, then lasers just aren't very useful weapons (and a quick glance at EDL and Ash's answers will confirm this). A pulse laser needs to deliver enough energy to vapourise a chunk of the target, and deliver enough of those pulses in a short enough time to carve a hole through the target. Your question presupposes the existence of consumer-grade, effective laser weapons, so that's what I'll run with.
A low powered laser might deliver, say, twenty pulses of 20 joules each in under a millisecond. Focussed down to a spot less than half a centimetre across, a short enough pulse duration will in fact drill a hole through meat. Not a big hole, or a wide one, but it should do the job. A longer pulse train would be preferable for drilling bigger holes, as would better focus.
Peak power will be enormous... 10-20MW, probably. Pulse lasers need that kind of massive power because they need to turn room-temperature matter into hot gas or plasma. You might not want to refer to the weapons as a "20MW pulse whatever" though... 400J would do a better job of informing people about the weapon's capabilities. Maybe "20x20" would be better, including both pulse energy and the number of pulses in a shot.
If you wanted to be more pedantic, it probably wouldn't be a "rifle" either. Rifling on lenses isn't useful! It'd probably look more like a little video camera than 22LR rifle. Here's a vintage super-8 that seems like a reasonable proxy:
(a laser weapon would probably have a trigger guard, mind you)
Not shown: cooling vents. There might be a little fan to provide forced-air cooling to the heatsink that stops the laser frazzling itself as well as whatever it is pointed at.
The eyepiece for the reflex gunsign is at the back; you can't see it from here. The front element of the lens is ~40mm across. A civilian weapon might sensibly produce a wavelength of 1000nm... near IR, invisible to human eyes. It blinds by burning the cornea rather than the retina, making eye damage potentially repairable by surgery. At this wavelength, the diffraction limited range for a 5mm diameter spot (about the largest you'd want for zapping pest species) would be ~160m, but real-world range would be probably more like 100m and maybe less. This seems roughly comparable to a 22LR, though the (probably) shorter effective killing range of the laser is more than made up for by the fact that it has negligible flight time, no bullet drop or windage, and as it uses a reflex gunsight (eg, you look down the barrel at the target, using the same set of optics) you'll hit exactly where you're pointing.
At very close range, say 20m or less, you'd have no problem blasting a hole clean through an unarmoured human, or fatally wounding big game. At maximum range, the wound could be fatal for humans, but I wouldn't rely on it. bad news for raccoons, though.
(note that at longer ranges, the laser is still dangerous, it can blind and burn and seriously wound, though it is unlikely to deliver an immediately fatal wound even to small game)
You could probably have a folding stock on the back if you wanted, but for this sort of weapon and purpose you probably wouldn't need one. If battery technology hasn't marched on enough (and current advances suggest it probably will) a stock might be a good place to put the battery.