What year models can a 2008 engine go in?

Honestly, use the money to buy a complete, running car. Unless you can do 100% of the work yourself, it will cost you more to swap the engine and transmission into another car. Between the time you spend trying to find another car the engine will fit into, then actually doing the work... Save yourself the money and effort and sell the wrecked car for scrap.

We are doing the work ourselves. We have weighed out so many options to go the cheapest route. Believe me that was gonna be my first move but yes we will be doing the work ourselves. Thank you

Find an '08 Cobalt LS or an '08 Pontiac G5. They are the same car. Anything else (even different years) will cost you money when you find the inevitable bits and pieces (sensors, electrical connections etc.) that are slightly different from your car. Changing the engine out is a huge job, and not likely worth the trouble as has been mentioned. The labor time in a shop with a hoist and all the proper equipment is 15-20 hours, just to give you an idea of what you're getting yourself into. Good luck.