Try the Family History Library "Internationl Genealogy Index- IGI" at the LDS-FHL website. You can narrow it down to Georgia and choose to search for just marriages; narrow it by a time frame also.
Only prob is you won't be able to narrow the search to Washington County so you'll have to go thru the search results page for page. That might be ok especially if the marriages your looking for happened in a neighboring county.

Good luck