Frankly, you don't even need to worry so much about type advantage. Just do a bit of level grinding on some neutral Pokemon (get a Purrloin to Level 20, for example), and you can easily take down the second gym. Right now my team on Pokemon Black has (or will have in the near future):
Waruvial (Dark/Ground), Sigilyph (Psychic/Flying), Lampent (Ghost/Fire), Frillish (Ghost/Water), Larvesta (Bug/Fire), and Deino (Dark/Dragon). Is it a rounded team? Goodness no, but with enough elbow grease and level grinding and you can easily sweep the Elite Four with it.