If you are in love with that guy, why do you bother when he is born. Haven't you checked his birth date before loving him and asking now at the time of marriage? You are afraid that some bad omen will happen to you if you marry him because he was born on Amavasya. I feel that this is no true love and am sorry for being brutally honest.
Remove the religious superstitions from your mind and get married and live happily. A person's ability to succeed or fail in life/career/profession does not depend on the day he was born or to the astrological aspects like raashi, thithi, nakshatra etc (as far as I believe). It depends on the person's ability, hard work and sincerity. Do you love a person by checking all these dates, nakshatras, time of birth, the lunar calendar time at birth? I guess no but when it comes to marriage people check all these, ironic.
Amavasya is not at all an inauspicious day. It is just an absence of Moon. As Sadhguru said, you feel the importance of a person only in his/her absence. Similarly, the absence of Moon on Amavasya makes her presence more than pournami. We miss Moon so much on that day. Amavasya is also considered as the day of liberation because something new will happen on that day.
Forget all these rational thoughts about marrying your guy who was born in Amavasya. Nothing will happen to you and if you have that immense love towards each other and if you have that understanding, your relation will blossom.
Dr. V. Shashikanth