Gen 2 Poké Balls as in the Apricorn Balls that werefirst introduced in G/S/C, but are also available in HeartGold / SoulSilver.
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You can trade from HG/SS to D/P/PL with the Pal Pad but youcannot trade the pokéballsas the Pokemon can’t hold it.>While Apricorns and the Poké Balls that are made from them can be held by a Pokémon in Generation II, this is not allowed in the Generation IV remakes, as these items are not programmed into the other games of that generation.-Bulbapedia
So, you cannot trade them into the Sinnoh games. If you trade a pokémon in a HG/SS pokeball, it will be a plain regular one when it goes to Sinnoh. I’m not sure if you can even trade Pokemon now, I think they shut off the wi-fi, but not completely sure about that.