Spotsylvania County voters elected Conway to represent them in the Virginia House of Delegates in 1847 (a part-time position), and re-elected him twice, so he served until 1850.
He also taught at Fredericksburg's Methodist Episcopal church for many years and led the city's Young Men's Christian Association.
Some gave him credit for suggesting the Virginia delegation support Franklin Pierce, who won the presidential nomination on the 34th ballot.
[9] Conway ran for election to Fredericksburg's city council in March 1855, but all the seats were swept by members of the Know-Nothing Party.
[10] On February 19, 1857, Conway was elected as judge of the 8th Virginia Judicial Circuit (which consisted of the counties he had represented in the Constitutional Convention as well as Essex, King and Queen, King George, Lancaster, Richmond and Westmoreland Counties in the Northern Neck of Virginia), filling the vacancy caused by the resignation of Judge John Tayloe Lomax.
However, shortly after he held his first court session, Conway experienced a sore in his left cheek which was diagnosed as cancer and eventually killed him, despite treatment in Baltimore that may have included removal of part of his lower jaw.
Artist John Adams elder drew a portrait of Conway which was sold as a lithograph in local stores for $1 each.