Pull the manifold and soak the stud in penetrating oil. Let it sit a day and soak it again. Wait another day and then grab the piece still there with some vice grips and try to turn it. If it doesn't move, you may have to apply some heat from a propane torch but be careful with all of the flammables there. Try to ease it out by working it back and forth. Worst case scenario is you will have to pull the head.
After reading the initial post again, I realized you were talking about the stud in the manifold, not the head.
You should pull the manifold and work on it. It really isn't that hard. Just make sure you soak the manifold to head bolts before you start to remove them. For the stud, a trick that has always worked for me is to heat it up till it's red hot. You will have to use an oxy-acetylene torch to do this. Turn off the torch and then spray the stud with WD-40 or penetrating oil. Do that 2-3 times and they usually come right out.
Sorry for the initial mis-understanding.