Amy, if we are talking about mixes (like International), you want to stay away from them, as they usually have partially hydrogenated oils as their main base (same with Coffeemate and many other mixes).
On the other hand, if you are talking about real coffee that's either flavored (on the beans) or has something like French Vanilla SF syrup in it, that should be fine, even in P1. Just make sure that you stick to no more than 2 servings of caffeine a day.
I love getting a decaf, skim milk latte with SF syrup in it at coffee places...it's expensive, but it's a very nice treat when I feel a little deprived in P1. You can even put cinnamon (as long as it doesn't have sugar in it) on top. Yum!