I don’t have a son named [name]Zachary[/name], and the [name]Zachary[/name] I know best has a little brother ([name]Ryan[/name] [name]Charles[/name]), not a sister… and the other [name]Zachary[/name] I know is an only child. So not sure if that’s helpful. But I did have a friend who had twins, [name]Zachariah[/name] [name]Lucas[/name] and [name]Catherine[/name] [name]Elizabeth[/name], so I think that’s cute. They went by Zachy and [name]Lizzie[/name] (they’re still under two years old, so I think the cutesy Zachy could still suit him, lol).
As for new suggestions, [name]Eliana[/name] was my first idea. Hebrew in origin, I believe, with very adorable nicknames (my favorites are [name]Ella[/name] and [name]Annie[/name]), but it ages gorgeously. And it’s definitely American enough! I think [name]Zachary[/name] and [name]Eliana[/name] are a gorgeous set! 
Other ideas I had:
[name]Julia[/name] (Biblical–I don’t know if it’s Hebrew enough, though! I love [name]Zachary[/name] and [name]Julia[/name] together, though!)
[name]Abigail[/name] (too common?)
[name]Eve[/name] (I think this is gorgeous–[name]Eve[/name] [name]Madeleine[/name] [name]Ruby[/name] just got nixed from my list, but I think it’s gorgeous, and [name]Zachary[/name] and [name]Eve[/name]/[name]Zachary[/name] and [name]Evie[/name] are adorable together)
[name]Hannah[/name] (very common, but it seems to be received quite well! And its popularity is diminishing…)
[name]Liliana[/name] (I dunno, lol, lilies seem to be quite a Biblical idea–I don’t know how prominent it is in Jewish culture, but a fairly common name for the [name]Messiah[/name]/[name]Jesus[/name] in the [name]Christian[/name] culture is “[name]Lily[/name] of the [name]Valley[/name]”)
[name]Rachel[/name] (kinda dated to some, but I love it, and I think [name]Zachary[/name] and [name]Rachel[/name] is great)
[name]Liora[/name] (I thin this is great, and it’s one of my top 3 Hebrew girls’ names ever! I think [name]Zachary[/name] and [name]Liora[/name] is great, and [name]Liora[/name] is transitioning into American name culture well, I think, so I think it would work)
My all-time favorite Hebrew girls’ name is [name]Ayelet[/name]. I LOOOVE it. And I think [name]Aya[/name] or [name]Lettie[/name] would be a fabulous nickname for it. It has a great meaning (dawn), and I think it fits in with today’s trends. On another baby name site I’m a member of, it wasn’t particularly well-received, but I think it’s great! I actually hope to name my first daughter [name]Isabelle[/name] [name]Ayelet[/name] [name]Grace[/name].
[name]Zachary[/name] and [name]Ayelet[/name] are really cute, I think.
I am pretty sure those are the only ideas I have right now! Good luck with your hunt!