Latios

You could use Trapinch, as cheating mentioned, or another good couple of Pokemon are Wobbuffet with shadow tag, or a very quick Zubat family member with mean look. I just nabbed it with a masterball, so I've never tested the Wobby or Zubat/Golbat/Crobat idea :(

Trapinch. Get a trapinch from the desert, and then the stupid bird thing can't run because of Arena trap, Trapinch's ability. Train Trapinch till it's on level 35 or 40, but don't let it evolve, or it'll lose the arena trap ability. Then go find latios, weaken with trapinch, and then keep throwing ultra balls at it.

Latios is difficult to find. Got to have lot of patience. But once you have fought it for the first time & even if you haven't managed to catch it, it's area could be seen in Pokedex. You move in & out of the Pokemon centre till it comes to your area. The Pokemon mentioned like wobbufet & crobat or golbat can prevent latios from fleeing but not for long as they are weak as compared tn latios. You need a really speedy psychic Pokemon like Kadabra, who can learn hypnosis as well as Ice beam.
Have lot many Ultra balls, but with above combination it's quite easy.

Using golbat with mean look or wobbufet with a shadow tag are some ways. But they are way too weaker than latios. Instead try using a very fast psychic Pokemon like kadabra who knows hypnosis and also some ice move like tm 13 i.e. Ice beam. It should be at least level 50 to have speed stats higher than latios.

use a wobbetfet or use mean look on it so its wont escape

Use trapinch he prevents fleeing with arena trap

Go to the route left of lilycove city where there is grass , you must have wobbufett .I caught my latios in a pokeball because I had 99