I've drank my first coffee of the day and immediately suffered an intense desire to nap. Coffee just isn't a very intense tool for the job.
I think the awake/alert factor I get from having my morning coffee at this point is a learned response, not a chemical one; a decaf coffee is just as good at perking me up in the morning as a non-decaf. If it weren't for the headache spikes hurled straight through my brain by satan himself I wouldn't even bother.
Edit: That's not true, I actually do love the taste and ritual of making coffee too; it's a whole thing to me. It's like a Japanese tea ceremony, but with coffee.
But sometimes, when no one is looking? I make a third cup.