Not that I can think of, coffee can actually help decrease constipation because of the stimulative effect it can have on the bowels.
Do you add anything else to your coffee? Is there any thing else you eat when you have additional cups?
Also, does she just seem to have issues (grunting, etc) or are there actual issues, and when it finally comes out they are hard nuggets? If when she does have a bowel movement, the stools are normal and not hard nuggets, then she isn't constipated.
I'm not certain about the caffeine from coffee. I know that any time I drink chai tea, it would affect my son and make him fussy. I do know that coffee helps adults go; I'm not sure about babies, but it does seem if she's having issues going, you could also fix this by learning and trying some elimination communication with her. The position used in EC is a deep squat that you're holding her in arms, which actually helps them to poop more easily. So it's something to maybe try out part-time during the pooping so that instead of laying down on her back and going in a diaper, she can go in a squatting position with you holding her over the toilet. It might help with the constipation.
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