During this era there was only one newspaper in Maryland. The "Maryland Gazette" began publication in 1727 and was based Annapolis. It is possible that New Market was mentioned after it began to appear on maps in 1776. A fairly complete set of the "Maryland Gazette" newspaper images are online at the Archives of Maryland Online.
1776-1789 - in progress...
Maryland Gazette -14 April 1785 -
In pursuance of an act of assembly passed last session, will be sold,
on twelve months credit, on bond with good security, at Cambridge, in
Dorchester county, on Wednesday the fifteenth day of June, if fair, if
not the next fair day, the following tracts of land, viz. New Market,
with dwelling and out houses, containing twenty-two acres; Bennett’s
Pasture, six acres, adjoining; Green Timber Yard, sixty-five acres, all
on Hungre river; Hog Quarter, two hundred and fifty acres, on Blackwater.
Charles Steuart, administrator of John Bennett.
1790 - No East New Market entries. One entry for Dorchester County (Vienna).