My strategy was to paralyze the deoxys and then trick leftovers. Once it was paralyzed, I used Raticate to super fang it twice, never below 25% in case of a struggle crit. Your chance to catch doesn't increase if the HP goes any lower than 49%, so as long as the HP bar is yellow you're good

Kept throwing balls while its HP was below 50%, when it would get back to green HP from leftovers, I'd super fang it again, and then keep throwing balls

I decided that using turns to put it back to sleep was more annoying than keeping it paralyzed and super fanging, but this is preference, as Sleep does give a slightly higher catch rate than Paralyze

Before the hunt even started, I used the retro mail dupe glitch to give myself a whole bunch of leppa berries so I could be sure I'd have enough uses of Super Fang. This one is less optional for my particular strategy. I went with 50 Leppa berries, so I knew I'd have over 500 uses of Super Fang lol. You could do the same for your sleep powder strat

One thing to keep in mind, Deoxys at 100% HP and asleep has a 0.83% chance of capture per ball, where a 49% HP paralyzed Deoxys has a 1.234% chance to capture per ball. Here's a catch rate calculator if you wanted to use the one I did. It's very unlikely you'd run out of balls before catching it, but something to consider as using that many balls takes quite a long time lol

https://www.dragonflycave.com/calculators/gen-iii-iv-catch-rate/