One cannot generalize the concept of hardness to a single proton in a meaningful, or at least unique way.
The hardness of materials is a measure of the yield stress, which is related to the chemical bonds in the material. A single proton does not have a yield stress so it doesn't have a hardness.
Not sure the question makes practical sense. Measures of hardness for macroscopic objects like samples of diamond depend on pressing the sample with another macroscopic object, which is not something that you can do with a individual nucleon. Nor can you trivially re-phrase the question in terms of, say, stiffness of the equation of state because there is no unique answer for a proton.