@VioletPie, what attracted you to Sweet Briar and what did you love about it enough to make you commit? If you mention those things it might be easier to help you find some matches. The closest likenesses to SBC might be the nearby women’s colleges Hollins and Mary Baldwin, but…those schools might not be on the most stable of financial footing either. Agnes Scott is also lovely with a beautiful campus and very diverse students, but it’s not rural like SBC, which seems to be an attracting component for you.
Another suggestion is Wesleyan College, a small liberal arts college for women in Macon, GA. Other small Southern women’s LACs are Stephens College (MO), Columbia College (SC), and Salem College (NC). However, some of these colleges might be facing similar financial struggles as Sweet Briar because they do have similar profiles - small, sometimes tiny enrollments; smaller endowments; high acceptance rates; and low student yields.