I just came from the local library in Ripley. In the book Brown Co.,Oh. Marriages 1818-1850 there are no marriages listed between the Richard Brown and Louise Williams. In fact there are no marriages between the Brown and any Williams.
There are, however, many Browns listed. I had the pages run off and will post them here if you like.
I also went to the Adams Co.,Oh Marriage books and again found nothing on the ones you were looking for.
I did find this in a book of marriages by Squire Thomas Shelton of Aberdeen 1822-1854: Brown,George X to Caroline Green 27/August/1846and Browne,Alfred M. to Martha James 27/December/1846.
I don't know how familiar you are with or if you have heard of Squire Shelton. Aberdeen,Ohio was a "Gretna Green",taken from the same named place in Scotland. Here you could get married and bypass a lot of red tape such as all the bonds or maybe underage or lacking parental consent.
Well, a lot of the records were never formally recorded. In recent years the papers from 1822-1854 were found and donated to the Library in Maysville,Ky. It is possible your relatives could have married there.A James Beasley also did this. I believe he owned a river boat and would cross couples from Ky. to be married.
As a matter of interest, Aberdeen is again calling itself the Gretna Green and will have it's 3rd(I think) festival soon and anyone can be married there or repeat there vows. A marriage license is required, of course. Last year I believe 1 couple was married and 1 renewed their vows.
If you have any other clues for me such as dates,places or such maybe I can find something else.
Sorry I didn't find what you needed but will post the Browns if you like. Eva