Give the Black Apricorn to Kurt in Azalea Town but only when you defeat Team Rocket the first time.
One way is to take Black( I think) Aprcorns to the guy in Azalea Town and have him create the Heavy Balls. you have to wait a day for it to finish first beat slowpoke well.
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you can only get cherish balls on event Pokemon they are not obtainable
you cant there is only one
In Pokemon Emerald, to obtain a Heavy Ball, you need to visit the Safari Zone extension in the Hoenn region. The Heavy Ball is a special type of Poke Ball that is more effective at catching heavier Pokemon. You can receive the Heavy Ball as a prize for participating in the Safari Zone's catching contest or by talking to the Safari Zone Warden after catching a certain number of Pokemon in the Safari Zone.
In Pokémon HeartGold and SoulSilver, the PokéBalls that you can get are: Poké Balls, Heal Balls, Great Balls, Net Balls, Dusk Balls, Friend Balls, Level Balls, Moon Balls, Heavy Balls, Lure Balls, Fast Balls, Luxury Balls, Ultra Balls, Love Balls, Nest Balls, Premier Balls, Quick Balls, Repeat Balls, Safari Balls, Timer Balls and Master Balls.