Question for a Recruiter or Army Reserve Career Counselor

You won't get it as a USAR contract incentive. However, there are units out there with Airborne slots. Closest one I know of to Pittsburgh is the 422d (I think that is the number) CA BN in Columbus, OH. There is also one in Ft Dix, NJ, the 404th CA BN.
You won't be able to get it in a contract, but there are units out there who can both train you and get you jump every other month.

You could transfer to a National Guard unit. I believe that there are SF battalions in West Virginia, Maryland, and Kentucky that are part of the 19th or 20th Special Forces Groups. Otherwise look at a Battlefield Surveillance Brigade. They have an Airborne LSU Troop in each Brigade. Otherwise look for a LRSD unit. All of these units may have long waiting lists to get into them. Don't discount support units that might have Airborne slots (quartermaster units with rigger sections, SF support battalions, etc...) You may need to switch to a new MOS. Unfortunately, finding an Airborne position in the USAR is tough. More options are available in the National Guard and the education benefits are better too.

SPC Voye,

You have a couple of options for getting the school that you want. One is to find a unit that has Airborne positions. You can go to your local Career Counseling for assistance in finding one. The other method is to join a Drill SGT unit. Once you get DS qualified, you can volunteer for mobilization. I have been told by people at Fort Benning that if you are on orders as a DS there and you prove yourself (aka DS of the cycle, quarter, year) then you could be allowed to attend Airborne school while you are there. (I do know one person that was able to do this).