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Now, there is another trick to finding them. You must have completed the Pokemon League at least once and obtained the National Dex from Oak. If you have done that, you can find them in Kanto's wild. They'll be at Level 50, so you'll want to bring about two Pokemon that is 50 - 55 in level and knows Hypnosis, Mean Look, and False Swipe. Marowak would be good for those going after Raikou or Entei, and Scizor for those who are going after Raikou or Suicune. You don't want a Scizor going up against Entei.

Once you've encounter them, put them to sleep so that they will not run. Yes, they will still run. Mean Look should follow directly after so they CANNOT run at all. Then, switch to Marowak/Scizor and False Swipe them down to 1 HP. Switch back to the Hypnosis guy and begin hurling those Ultra Balls until they wake up, or you catch it. If they wake up, put them to sleep again. It's just like catching Latios/Latias from R/S or the dogs from G/S.

Do you still have a Master Ball? Are you planning on attending a Nintendo event to get Deoxys? If you answer yes and no, grab that ball and use it on the dog. It will make things a lot quicker.

If they manage to escape before you can use the initial Hypnosis/Mean Look, you can find them again by checking their location via your Pokedex. Just finding them again around Kanto is the harder part. If you have a friend with one of the other dogs, trade yours for his and find another friend who has the other dog that you don't have. Or, if you're lazy like me, find them in Pokemon Colloseum and trade them to your version.

Good luck!