Honestly, one cup of coffee probably isn't going to make a difference (but everyone is different). When I was going through my fresh cycles a number of years ago, I had to do 2. The first one I followed everything to the letter, including completely cutting out caffeine, and got a negative. I was so miserable for the first round that with the second I was a bit more relaxed about the recommendations and drank one cup a day, and ended up pregnant with my daughter. Maybe taking the stress off of myself a bit helped?
I did FETs more recently and took a pretty relaxed approach - I definitely couldn't cut out caffeine completely as I work full-time and had another kid to care for. 1 chemical, 1 ectopic, and finally the last one took and resulted in my now 4 month old son. I don't think my caffeine consumption affected any of that.
Unfortunately there is no one thing that will ensure that your cycle will be a success. I think that managing stress and trying to stay relaxed is probably a bigger factor, so if one cup of coffee per day helps you do that, then do what you need to.