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No tricks. Sorry about it but your best bet is to hunt until you find a Chansey. I got lucky on my first try and bagged a Chansey on Route 14. And it had a lucky egg attached. Showing that Chansey to the lady won't give you a lucky egg either, it gives you a lucky punch.
Just because I'm a girl, doesn't make me any less skilled at gaming.
During a Chansey swarm, have a fainted Butterfree (compound eyes ability) in the first slot in your party. In the second slot should be a Stantler (or anything else) that has the Frisk ability.
The compound eyes ability increases the chance of wild pokemon holding an item if it's in the first slot in your party. The frisk ability tells you what the item the pokemon is holding.
Encounter a Chansey. If it says it's holding an Oval Stone (or doesn't say anything), run. If it says it's holding a Lucky egg, catch it. Use your standard catching techniques (bring some Love Balls and a male pokemon). Now you have a[nother] Chansey, and a Lucky Egg.
Just wait for the swarm.
Now playing: Pokemon Red (Black/White), The Beatles: Rock Band, Earthbound (1.5x enemy stats/hard mode hack)