I am a male convert and my family is not Muslim. Who can represent me in making a proposal?

You can propose yourself, or ask a Muslim you respect, such as a religious teacher or close friend, to act as your representative. A man does not need a wali (guardian) to marry, so not having Muslim family does not prevent your proposal. Many converts ask for help from an ustaz at a convert guidance centre or a mosque committee member. If your non-Muslim parents are willing to attend as a sign of their blessing, that is a good thing and should be welcomed. Tell the woman's family honestly about your background from the start. Your openness will make it easier for them to accept you. See using an intermediary to propose.