After looking at Torchic's moveset, TMs, items, and such, I've come to the conclusion that It's basically impossible!
At this point in the game, Torchic just doesn't have any moves that can do good damage to Rock types. Attack EVs won't help much, since your moves won't be effective against them. Defensive EVs won't help much either, because Torchic is going down after a few Rock moves. Unless you get god lucky RNG that Roxanne misses all her attacks, your attacks somehow kill all her Pokemon, and she quits her job, you aren't winning. There aren't any good items that can make things easy for you unfortunately.
So yeah, get god lucky RNG or lose. It's just not possible Personally, I'd recommend starting over and choosing a different type or making the rules a bit more flexible (cause yeah, you don't got much options and you won't be getting a new member any time soon). Hopes this helps Ig...