Things You'll Need
Instructions
Go to the nearest Pokemon Mart and stock up on Ultra Balls and Dusk Balls. Ultra Balls are generally effective at catching Pokemon, and Dusk Balls are designed for catching Pokemon in caves. Buy some Revives and other healing supplies (like Potions) if you have the extra money.
Go to the nearest Pokemon Center and add a Pokemon who has a move that can inflict Sleep or Paralysis on an enemy Pokemon. Both Sleep and Paralysis make it easier to catch wild Pokemon. Bring a Pokemon that has the move "False Swipe" with you as well. False Swipe damages Pokemon, but never kills it (the enemy Pokemon will always have one hit-point left, no matter how much damage False Swipe does).
Return to the Stone Pillar in Mt. Coronet. Move the Pokemon with the Sleep/Paralysis move to the front of your party so it goes out first when you start the battle. Save your game before progressing any further.
Approach Dialga and press the "A" button to start the battle.
Use the move to paralyze or put Dialga to sleep immediately. Keep using this move until Dialga is asleep or paralyzed.
Attack Dialga using weaker moves to bring its health down so the bar is red. You can also send out the Pokemon with the move False Swipe to whittle away Dialga's health down to a single hit-point. The lower Dialga's health, the easier it will be to catch.
Use an Ultra Ball or a Dusk Ball on Dialga to catch it. No matter how low Dialga's health is, there's a chance it will break free. It's likely going to take several tries before you get it. Keep throwing Ultra Balls or Dusk Balls, and you'll eventually catch Dialga.