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Lead with a Synchronise mon, then swap it out for a male, Modest Cute Charm Mon with a fighting move of some kind, or skill Swap. The Synchronise effect applies so long as you just lead with the mon. Due to a glitch however, Synchronise's effect will continue nature matching incoming Pokemon even if the Pokemon is off the field so long as it was originally in the first spot, but it matches incoming natures of Pokemon with the CURRENT Pokemon you have out. The Cute charm effect applies so long as your charmer is on the field.
With a fighting move, HA Eevee will trigger Anticipation, though Skill Swap and a truckload of Leppa Berries is a poormans substitute.
You will still have to deal with the 50% success rate of nature matching.
