My mother sang this song to us too. I can remember the Chinese girl, but not the coat of tan.
Down in Bongo Bay where the good ship lay, Danny met a Chinese maid one day And he filled her trunk full of Yankee bunk, Told this maid a lot of Yankee junk. Yip Sing How cried Danny with great glee. You have made and awful hit with me. On Broadway you'd be in opery. Then this yellow maiden said You're off of Californy full of hokey poke. You're off of Californy full of hokey joke. You got a gal in Frisco yet you flirty, flirt. No Chucky's got now washing for an extra shirt.
The little coat of tan was before the Chinese girl, but I can't remember it either.