Regarding "The Happy Miner", to the tune "I Get in a Weaving Way": Christy's and White's Ethiopian Melodies (1854, p.38; search Google Books) contains the song "Sally is de Gal for Me" with the chorus:

When I get in a weaving way,
Spend my money free,
Oh, here's good liquor! come and drink!
Oh, Sally is de gal for me!

Sadly, no score given.

Per the thread here on "Jawbone", N.L. White, in Negro Singers' Own Book (1846), said "Sally Is de Gal" was sung by Jim Carter. So while the tune for this song may still remain elusive, there are a few more clues to work from.