I have been working for a long time on finding the parents of Elijah Hillman Green.
I have fairly strong evidence - but not proof - that his father was Jesse Green, son of George Green ( a soldier in the Revolution from Halifax Co., NC) who was the son of Daniel Green who migrated to Halifax before the war from Stafford County, VA. The only record of Jesse Green's marriage was to Sarah Shearin in 1818, six years after Elijah Green was born. But I believe that he had an earlier marriage which has not appeared in any records. At that time in Halifax Co., NC a marriage bond was not required for a church wedding and there would be no record unless it was in a family bible or in the church records. So the lack of a record of a wedding means nothing.
I will be glad to share what information I have if you will email me at firstname.lastname@example.org