Try looking up the photographer or photography company in Raleigh directories - that will give you an idea of the time period.
In fact, I was bored so I've just done it for you.
John W Watson was a photographer in Raleigh at 131 Fayetteville in 1886 and 1887. Unfortunately, there are no Raleigh directories on ACOM before 1886 and after 1887, it jumps to 1899. By this point, Watson is no longer listed so probably out of business or moved out of the city. But you know the photo was taken before 1899, possibly during the 1880s. You may be able to find other directory record years elsewhere to narrow it down more, I only looked on ACOM.