The correct option is
B He will come provided it does not rain in the evening.
Option A: "In spite of"
is a prepositional phrase which is used to express the contrast between two actions/ events. It indicates something which happened/ will happen although something else might have prevented /might prevent it. "In spite of" is always followed by a noun/ pronoun; however, here it is followed by a verb (does not rain). Hence, this is grammatically incorrect. Further, this is a prepositional phrase and not a conjunction. Hence, this option is incorrect.Option B: "Provided" is a conditional conjunction (also a subordinating conjunction) which connects two sentences when one sentence describes something that did/ will happen if the condition of the other sentence is satisfied. In the given example, "he will come" is conditional upon "it not raining in the evening". Hence, "provided" is the most appropriate conjunction to be used. Option B means the same as: "He will come if it does not rain in the evening", and is the correct answer.
Option C: "So that" is a subordinating conjunction which is used to express cause or reason. It is used to connect two sentences when one is the cause of the other. In the given example, one sentence is not the cause/ reason for the other. Hence, option C is incorrect.
Option D: "However" is a co-ordinating adverb which is used to connect two contrasting independent clauses. Here, the two clauses are not contrasting. They are dependent because one sentence is conditional upon another. Hence, this option is incorrect.