Tips on Buying Cars: Potential lemon car, legal jargon, lemon car

Question
We purchased a car 5 days ago for our son.  We paid $2600. for it after some negotiating. This was a private seller.  The title has been signed but not yet officially transferred. Our problem is that we took it to our mechanic to have it looked at and unfortunately, it appears to burn quite a bit of oil.  It smokes quite a bit when you start it up, but then clears up after it is warm.  I remember when we got there to look at the car, it had been started and was warm already.  We called and told the sellers we want to bring the car back and they said they would give us $200. towards repairs.  I'm just wondering if we have any other recourse.  We live in Illinois.

Answer
You'd first need to check with the state agency in Illinois that regulates vehicle purchases and possible lemon-law coverage; they're different in each state, and here in New York it's the Attorney General's office.  Few (if any) states offer coverage for private-sale purchases, so don't be surprised if you're on your own.  I'm thinking you're only form of recourse is to hire an attorney and prove in court you were defrauded into buying the car (based on the fact that it was already running and warmed up when you got there; such actions could be construed as an attempt to hide a known problem with the vehicle, which is illegal).  In the short term, do you have an attorney friend that might be willing to write up something you could give to the sellers, a letter worded in a way that might just "convince" them to give all of your money back?  You know, some legal jargon on official letterhead that would make them realize you're serious about going to court, getting a refund, etc...  I'm sure you know what I'm getting at.