Roar can be stopped by the abilities Soundproof and Suction Cups, or the move Ingrain. Of the Pokémon which can have one of these, only three can learn Block, without which the legendaries will flee: Abomasnow, Cradily, and Tangrowth.
Of those three, Abomasnow learns the sleep move GrassWhistle, Tangrowth learns Sleep Powder and Stun Spore, but Cradily can learn no sleep or paralysis moves. Abomasnow's ability Snow Warning ability summons hail which may kill the legendary before you're done throwing Pokéballs at it. None of the three are particularly fast, with 43 to 60 speed compared to Entei's 100 and Raikou's 115.
Alternatively, Umbreon and Absol can learn both Mean Look and Baton Pass. Use this to block the legendary from fleeing, then pass to something Roar-proof. Mr. Mime can have Soundproof and learn Hypnosis by breeding with Drowzee. The Bulbasaur, Oddish, Bellsprout, Exeggcute, Roselia and Carnivine lines can learn both Ingrain and Sleep Powder, in some cases by breeding, and all of those except Bulbasaur can also learn Stun Spore. Sunflora and Roselia can learn Ingrain and Stun Spore. Electrode can have Soundproof and Thunder Wave if you're willing to work at Battle Frontier for the TM.
Note that it requires some effort to give Umbreon and Absol both Mean Look and Baton Pass. You have to raise an Eevee to level 36 without evolving it to learn Baton Pass, then learn Mean Look as Umbreon at level 57. Absol learns both moves only by breeding from Umbreon. Absol's advantage is that he can be taught False Swipe and Thunder Wave by TM.