Pearl/Diamond Legendary Trio help?

Good question I had the same problem when I was catching them. There is no easy solution, I also became very frustrated. Yes, I suggest putting it to sleep rather than paralying it but, be warned it make still take a while. Put them to sleep and keep trying with ultra and dusk and timer over many turns. Three more important things you might not know. No.1 when you first start always try a quick ball before anything else(it might work) No.2 to increase your chances of capture always throw different , try to avoid throwing the same ball in a row. For example, after it is asleep with 1HP use a dusk ball then an ultra ball then a dusk ball and so on. Lastly, this I'm not sure about but maybe try the dusk ball at night too.