Can I season a cast iron pan on a charcoal grill?
Maybe you are using heat that is too high.  It really doesn't take that much.  A 375 - 400 F oven will do the trick.  Light coat of oil, heat for an hour.  Allow to cool in oven.  Wipe out.  Upside down allows excess oil to drip out (use a drip pan)...but you don't need that much to begin with.  There is no reason you could not do this on your grill.  For the first few uses, wipe out and scrub with kosher salt to remove cooked on bits.  Then give a light coat of oil and wipe out.  Once you have built up the surface it is fine to clean with soap and water.