I have a proposal from a man who is willing to revert to Islam. How do I know he is genuinely believing and will our marriage be accepted if he secretly reverts for love?
You never really know about people. Even in the time of the Prophet (S), there were hypocrites who pretended to be Muslim. Only Allah knows what is in the heart, and only Allah knows whether people will follow through with a lifetime commitment (such as converting to a religion - or, for that matter, having a lifelong marriage).
Many of the sahabah converted instantly. So if he converts tomorrow, he could be an Abu Dharr or a Salman al-Farsi. Or he could be... someone else. One way you can glean some idea of this is with respect to how he is with commitment in life, in general. Has he followed through on other commitments, or does he tend to jump around from thing to thing? This still doesn't give you a full picture but gives you some idea.
Also, people sometimes change throughout life anyway - there is no guarantee that the person you marry will be the same person forever.
So, you can never know for sure, but it is good to follow your intuition and good judgment and advice from people you trust and who have wisdom. If you are having doubts, possibly your intuition is picking up on signs that your rational mind is dismissing.
You could wait some time after he has converted (say, a couple years) before committing to the marriage to see how he does with Islam.
That said, it is not respectful to doubt that someone is sincere about his religious belief simply because he was not born into it (unless there are some signs that the person is insincere or not thinking straight), and respect is important for marriage. So this should also be sorted out before marriage.
It is not uncommon for women to convert at the time of marriage to a Muslim man and often they remain in the faith and become strong Muslims. Of course, the social situation and experiences of men are somewhat different, but just putting that out there.