Things You'll Need
Instructions
Keep a Pokémon close to (but not at) level 50 and equipped with the "Hypnosis" or "Sleep Powder" attack at the front of your party.
Use the max repel and walk around an area of tall grass where weaker Pokémon usually appear (such as the route between Pallet Town and Viridian City.) The repel will keep weaker Pokémon from attacking, meaning only the legendary dog will attack.
Use "Hypnosis" or "Sleep Powder" as soon as the legendary dog appears to make it fall asleep.
Switch to the Pokémon with "False Swipe" and use it to bring the legendary dog down to one hit point. Switch back to the sleep-inducing Pokémon.
Use an Ultra Ball to capture the Pokémon. You may need to throw several Ultra Balls to capture it.
Use "Hypnosis" or "Sleep Powder" again if the dog wakes up, and then continue throwing Ultra Balls until you capture the Pokémon.