"I would feel happy if we become friends." (become)
or
"I would feel happy if we became friends." (became)
or
"I would feel happy if we were to become friends." (were to become)
Update: or
"I would feel happy if we could become friends." (could become)
Perhaps related, I noticed a comment on another answer saying that imperatives are always in present tense. Is "become" an imperative in the examples above?