In my limited experience, it depends on what is causing your
tachycardia,
and what your
tachycardia is. Morning coffee might just speed your heart rate, or it could leave you more likely to experience tachycardia, or exacerbate your anxiety troubles.
What is it about your coffee that your Love, I wonder? If it is taste, and a little zing, you could always try decaf, or maybe mix 1/2 decaf with 1/2 regular, and limit your intake.