Could coffee be the reason my hemoglobin has been falling?

If your hemoglobin is low it's because you aren't getting enough iron. Go to a pharmacy and get some ferrous iron tablets or iron ferrous sulfate in the strength of anywhere from 27 mg to 50 mg should be sufficient since it's not that low. Liver is good to eat for iron, beef and even hamburgers, lima beans but antibiotics can inhibit the absorption of iron.