I purchased a small coffee plant last year, and this year for the past few months, it has had brown discoloration on the leaves (brown) and it spreads. This begins on outer edges and grows inward. The new top leaves are very green and look healthy.
Coffee Plant Showing Signs of Disease
Assuming your coffee plant is indoors, I would think that the problem could be lack of humidity. The symptoms you describe are commonly associated with the dry heated air found in most homes. If it isn't lack of humidity, the problem ccould be rust.. If it is rust, ground cinnamon, neem oil or an all-purposr fungicide should work.