You must follow Suicune to the following places if you wish to capture it.
First, it will be found to the north of Cianwood city, next it travels just outside the entrance of Mt. Mortar on Route 42 (You will have to go to the middle entrance and use cut on the tree). Afterwards, it will head to Kanto where you will see it in Vermillion City soon after you arrive, Next it will head to Route 14 where it will escape for the final time to Bill's house on Route 25 after Misty has returned to her Gym. This will be your first chance to fight it.
If you happen to defeat it, it will re-appear at the Burnt Tower where you first met it.
Hope this helps :]
•You first run into Suicune in the Burned Tower in Ecruteak City. You have to have seen Suicune here in order for Morty to go to the Gym, so this one is really guaranteed.
•The second time you can find Suicune is just north of Cianwood City. You'll find Suicune on the northern part of the city. As you approach it, it will flee, but then Eusine will battle you.
•The third place to encounter Suicune is on Route 42, just outside of Mt. Mortar. There's three Apricorns hiding behind a tree you can cut down — as well as an elusive Suicune! Chop down the bush and then Suicune will run off.
•The fourth place you'll run into Suicune is in Vermilion City, right on the dock leading you to the S.S. Aqua. Be sure to go there and you'll run into it as well as Eusine.
•The fifth and final location you'll need to find Suicune at is down on Route 14 in the southeastern part of Kanto, a bit east of Fuchsia City. You'll find it on the eastern part of the route as you head north onto Route 13.
Information from Marriland's HeartGold & SoulSilver Walkthrough.
