No, you can't. If you want to paralyze a Pokemon, it has to be awake.
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Simple either Do the special conditions like poison,paralyze, sleep and I say that you paralyze it and make it fall asleep and use a dusk ball or you could use the master ball that Cyrus gave you and you have caught a Giratina
Use Electric Types To Paralyze The Get The Life Low And Use Ultra Or Great Ball.
Simply weaken it to red HP paralyze it and use as many net balls as you can.
weaken it's health to red and paralyze it. use tons of pokeballs or other kinds.
Use master balls. Use a ton of ultra balls and put them to sleep or paralyze but master balls are your best bet since leaf green is harder than its original counterpart