This is very much a work in process and a complicated family to put together.I believe this John Geer (b. @1790) is the son of David Geer and Susannah MattersonMadison who married in Rutherford Co. @1770.David being the son of John Geer (d.1769)in Orange Co., NC.
John (d. 1769) is specualtived to be a descendant of George Geer of Connecticut, but the exact connection has not been made. (He may very well be a Geer of Dutch descent).
I know some have placed your John as the son of David (b, 1781 - Geer ID #390) and grandson of Solomon (b. 1760 - Geer ID #154), but their dates do not fit.
Please note this descent is my speculation and is not proven, but warrents more research.