I'm still trying to figure out exactly what Sweeney is being credited with "inventing," since African American banjos that pre-date Sweeney had the same basic design as the "modern" five-string banjo: a membrane stretched over a skin, a stiff neck, and several strings, one of which was a "drone" string. Was it that Sweeney used a wooden frame instead of a gourd? Or that he used a fretted neck? Or that he standardized the five-string arrangement (African American banjos had a varying number of strings)?
If we're going to give Sweeney credit for making the first banjo in the country because he used a wooden frame instead of a gourd, it seems like we should also give credit for creating a new instrument to whoever made the bedpan banjo, the toilet seat guitar, and the horse jaw fiddle that are also on display in the museum.
This painting titled "The Old Plantation" (attributed to John Rose, ca. 1785-1795) shows an African slave playing a four-string (fretless?) banjo on a South Carolina plantation. The banjo appears to have a stretched membrane and a short drone string. As far as I can tell, it's the oldest depiction of a banjo in North America.