I'll only be focusing on girls' names, since there weren't too many boys' names listed (the above graph that shows Zayn in the 1880's is actually in error!)
Zainab - "beautiful"
This attractive Arabic name has popularity in Islamic culture due to its connection to relatives of the prophet Mohammed. An unusual b-ending rounds out this feminine name - other than Jacob, nothing is jumping to mind that's similar. I'd recommend this highly, especially those looking for something religious, unique, or meaning-oriented.
Zahra - "flower"
An excellent alternative to Sarah, this lovely name might have a few drawbacks - spelling will always be an issue, and the connection to celeb-baby Zahara Jolie-Pitt might raise some eyebrows. But in the right place, it could work wonders.
Zella - "lacking nothing, one who knows the way"
This name comes from the central African language Bobangi, and could be a great way to honor connections to the area. Zella isn't too far off from popular Bella or Ella, either, and won't be out of place on a playground.
Zelda - "gray fighting maid"
Zippy and bold, Zelda is a great choice for a confident, daring little girl. The connection to both the eponymous video game and writer Zelda Fitzgerald of the Jazz Age will let the name age gracefully with its carrier.
Zelma - "God helmet"
Doesn't have quite the pizazz of Zelda or Zella, but could be a great way to honor an Anselm. The auditory connection to Selma might also be a plus.
Zora - "dawn"
Fantastic sound, fantastic meaning, fantastic namesake - Zora Neale Hurston, the author of Their Eyes Were Watching God. This Z-name deserves an emphatic comeback.
Zula - derived from Zulu, a South African tribe
In the lower 300's as of 1880, this name dropped off the charts entirely in 1936. Strong and memorable, it's definitely worth looking over.
What are your favorite Z-names?