With a cup of corn syrup, I doubt it'd be undercarbed.
One cup of corn syrup and 2 ounces of priming sugar would make me think just the opposite. Probably overcarbed, and possibly by alot.
I would have check the SG of the corn syrup and done some math, instead of just guessing. Here's an article from Skotrat that might be helpful:
Particularly for ales, some people enjoy the note added by using brown sugar or Demerara sugar for priming; the same weights should be used as for white sugar. For the adventurous, syrups can also be used, but the weights need to be increased to account for the water and different types of sugars present: honey (suggested extra 40% by weight), genuine maple syrup (+50%) or molasses (+80%). Furthermore, the results will be less predictable and carbonation will take longer. Some report that molasses produces a very unpleasant overpowering taste that only moderates after many months. You may need to experiment.
If you want to do your own tests on the relative effectiveness of various priming agents, you need to know: i) its strength at increasing specific gravity, and ii) its fermentability. To calculate the increase in specific gravity, take a litre (quart) of fresh water and dissolve the priming agent at the rate of 120 g/l (1 lb/US gall). For sucrose, this should give a solution with a gravity of 1047. Other sugars will tend to give lower values. The fermentability of simple sugars including honey is very close to 100%. Priming agents containing more complex sugars such as malt are not fully fermentable and the exact value will have to be estimated as best you can, but 80% is probably a good starting point.