I am reading an old history book "Relgion on the American Frontier Vol. II - The Presbyterians 1783-1840 By William Warren Sweet. I found it in my churh library. Wish I had Vol I. anyway here is what it says about the Covenatents.
Page 6-7.
Besides the regular Presbyterians by the opening of the Revolution here had come to be two croups of dissenting Scotch Presbyterians established in the colonies. The first were those who regared the settlement of 1689 as failing to give proper recognition to the national convnants of 1638 and 1643 and renouned both church and state. For a number of years they were without ministers and the sacrements but by 1743 they were able to form the Reformed or Covenanter Presbytery as organized in America. The other conservative Presbyterian body was the Associate Synod. This represented the first formal secession from the Church of Scotland which had taken place in 1733. Their secession was due to the growing centralization of power in the hands of the General Assembly and their protest against the strange and questionable doctrines which they claimed were being taught by professors of theology. It was in 1753 that the first Associate synod was formed in America, which by the opening of the War for Independence had increased to tow presbyteries and thirteen ministers. Just a little history on the Covenanter's in early America. I too have Scotch-Irish, and French Hugunot families I a working on.

Mary Ellen