All of these are possible, however each one provides a different nuance to the sentence. Also, each of these are auxiliary verbs and must have another verb after them. So in this case you could say "If it rains tomorrow, you could use my umbrella." Now, allow me to explain the difference between each verb.
"can" indicates ability and in some casual contexts, permission.
"could" indicates possibility or a suggestion.
"may" indicates permission.
"might" indicates possibility or likelihood of something to occur.
"shall" indicates a statement of certainty; as if that is the only outcome in the situation.
"should" indicates a strong suggestion.
Any of these would be fine, but think first about how you want to express it. Any of them would be fine. To me, however, in this context, "might" and "shall" sound slightly unnatural; Especially in the case of "shall," it sounds a bit demanding. I hope this helps. Let me know if you are still confused.