Get a Haunter/Gengar and level it up to a similar level as the wild Suicune.
Teach it Mean Look. Gastly learns Mean Look at Level 48, Haunter learns it at Level 64, and Gengar learns it at Level 1, so you would have to use a Move Reminder.
Follow Suicune, (via locating its area in the Pokedex,) until it is on the same route as you.
Save your game
Enter the grass and attempt to encounter Suicune. Make sure you have a lot of Net Balls, Timer Balls, and Ultra Balls. Use Mean Look first turn. If Suicune flees before you use Mean Look, that means your Haunter/Gengar is not fast enough. Level it up more. Once you use Mean Look, Haunter/Gengar cannot die or switch out, because Mean Look will stop working.
Throw Net, Timer, and Ultra Balls until you catch it.
Hope I could help!