What you're looking for would be a Polaris Liberty twin, 600, 700, or 800 with VES (variable exhaust system). The 600 is often referred to as the "small block:" it's physically smaller than the 700 and 800. The 700 and 800, "big block" are easy to tell apart by the bigger recoil cover that houses the (belt driven) oil and water pumps. Polaris introduced those motors in the previous chassis as a 600 and 700, then 800 for a year or two, without VES. Those engines will bolt up provided you've got the correct mounts, and the only "problem" is they're less powerful than the VES variants. You can tell the VES motors at a glance, they have a casting that protrudes from the exhaust side with a black plastic cover.
The best motors in terms of reliability are the 600 and 700; the 800s tend to have a lot of crank issues. You'll want to find a complete setup (with air box, carbs, exhaust, ignition, and so on), and the clutches if you can. Buying a wrecked sled would probably be best if you can find one. Starting with a bare motor and having to buy the rest piecemeal might end up costing you as much as a comparable sled. Once you have all the right pieces, it's relatively simple to bolt it all up.