What about saying that the person is deficient without common sense? This use of the word without would give the sentence--He is deficient without common sense--the implication that the male is somehow wanting in completeness as a person because he lacks common sense. There are, indeed, people who could say this about others, particularly at certain job sites in which common sense plays an integral role in the decision-making process or in the operation of one's duties in a certain position.
In American English, at least, the only preposition that would really go in this blank would be "in." So we would say "He is deficient in common sense," which means that he does not have enough common sense.
I do not know if, in British English, you could say that someone is deficient at common sense or deficient of common sense, but neither of these would sound correct in American English.
I cannot think of any other prepositions that would even make sense in this sentence. "In" is clearly the preposition I would use to fill in this blank.