Hey! I can make up an answer!
The 1850s were the smack in the prime of the minstrel show, in which white actors smeared their faces with black makeup and impersonated African-Americans. To accentuate the big-lipped and wide-eyed Funny Slave character, especially since theatrical lighting was almost as archaic as the jokes they told, white greasepaint circled the performers’ eyes and mouths. The bulls-eye eyes reminded someone of a raccoon, and there you go.
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This phony baloney explanation was manufactured on the spot, but if somebody wanted to spread it as fact I’d think it was really cool.
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While pretending to research it I found the interesting factoid that, according to Moe Howard, Mantan Moreland, the bulgy-eyed, third funniest guy in the Three Stooges shorts, was considered for the role of Third Stooge after Shemp died. Since Moreland lived until 1973, we’d’ve been spared the depredations of both Joes.