There are four cemeteries in Langholm, the two you mention plus Staplegordon (the old name for the parish of Langholm) and the modern one by Skipper's bridge. Dumfries Family Society (
www.dgfhs.org.uk) have published Old Parochial Registers of Deaths and Burials for Langholm (£4.50). You can also buy the MI's of Staplegordon, Old Langholm and Wauchope from them.