Here are combinations that have all have the fastest "failure rate." Meaning the average time wasted if you don't successfully breed a copper dragon is only 2.45 hours.
Breeding Combination 1: CactusDragon + CopperDragon Failure Average: 2.25 hrs
Breeding Combination 2: CactusDragon + MagneticDragon Failure Average: 2.25 hrs
Breeding Combination 3: CactusDragon + MetalDragon Failure Average: 2.25 hrs
Breeding Combination 4: CopperDragon + PlantDragon Failure Average: 2.25 hrs
Breeding Combination 5: MagneticDragon + PlantDragon Failure Average: 2.25 hrs
Calculations done at http://dvcalc.pf-control.de/