Without access to Knock Off and Ice Punch on a Conkeldurr, what are the next best moves to run alongside Drain Punch and Mach Punch? Stone Miss and Payback are really the only things that come to mind.
Why wouldn't you have access to those? If this is in-game, I don't think this is the right place to ask this question. If this is not in-game, I won't further question why you wouldn't have access, and tell you what I think would be best. Earthquake is big, (maybe) Bulk Up, (if you have guts) Facade, any other elemental punch, and (if Stone Miss really gets to you) Rock Slide or Tomb (latter lowers speed). That is probably the extent of its movepool for most competitive purposes, but if you want to get interesting, there is Smack Down, Reversal, Poison Jab, Low Sweep (Lowers Speed), Brick Break, Focus Punch, and Bulldoze (also Lowers speed). Enjoy.
Ice Punch and Knock Off are Gen 5 tutors only. You can't really replace them with anything else because they are so vital to Conkeldurr. Payback is Knock Off but without removing an item. But nothing comes close to Ice Punch.
I'd go with Drain Punch/Mach Punch/Payback/Stone Edge if trying to use an AV set without tutors.