"Proposing to me makes him happy" is more natural.
However, neither makes much sense. Using the present tense suggests a regular or habitual action. Usually, someone proposes to someone else (hopefully) just once, not on a regular basis.
Yesterday, Bob proposed to me. I said yes. It made him very happy!
I assume you know that "to propose" when used on its own usually means "to ask someone to marry you".
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