What sort of necklace would look good with a black cocktail dress?

Depends on the occasion you want to go. For example, if it a party, a silver jewelry set or simple white pearl will be more beautiful Like These:

Vintage Imitation Pearl Crystal Jewelry Sets | Buy From Here[1]

YIKALAISI Natural Freshwater Pearl Jewelry Set | Buy From Here[2]

Women Wedding Party Jewelry Sets| Buy From Here[3]

For daily outfit choose something more simple and casual, that keep your look younger like these:

Crystal Happy Smile Face Pendant Necklaces | Buy From Here[4]

Four Leaf Clover Necklace | Buy From Here[5]

ZWC Chemical Molecular Pendant Necklace | Buy From Here[6]

Just all you need to avoid the dark necklaces and let the dress style talk. Have a great shopping.

Footnotes

[1] Vintage Imitation Pearl Crystal Jewelry Sets

[2] YIKALAISI Natural Freshwater Pearl Jewelry Set

[3] Women Wedding Party Jewelry Sets

[4] Crystal Happy Smile Face Pendant Necklaces

[5] https://www.touchy-style.com/col...

[6] https://www.touchy-style.com/col...