It seems like it's more the outside appearance of the Dollar General than what's sold on the inside that is disliked. Maybe the zoning board could suggest some different signs and store front appearance that blends with the Moultonborough area. Maybe copy the looks on the outside of the Moultonborough Country Store and Museum which has been there since 1783.
www.nhcountrystore.com
Probably, that faded yellow paint on the M-Boro Country Store may be called ochre color, or ochre paint, and possibly a Dollar General could do a good job of blending with period signs, and an historical color paint job. One good coat of historical paint from 1783 can change everything ...... if it's the correct color!