I’ve recently fallen for the nickname [name_u]Caro[/name_u]. What full names can you derive it from beyond [name_f]Caroline[/name_f]/[name_f]Carolyn[/name_f]/[name_f]Carolina[/name_f]?
Maybe:
[name_u]Cairo[/name_u] (it’s a place name so it sounds and looks unisex)
And then there’s the hundred and one variation of [name_f]Caroline[/name_f] and [name_f]Carolyn[/name_f].
But maybe you could do something along the lines of Cara [name_f]Ro[/name_f]semary where the initials/beginning sounds spell out [name_u]Caro[/name_u].
I hope this helped a little bit! FYI, I used the Nameberry thing-y for searching the names and just typed “[name_u]Caro[/name_u]” for the part where it said “contains”. You could probably find something if you type in “Car” as well.
I was thinking the same as [name_f]Elena[/name_f], first and middle names to create [name_u]Caro[/name_u]. I see [name_f]Carys[/name_f] in your signature, you could do [name_f]Carys[/name_f] [name_f]Ophelia[/name_f] nn [name_u]Caro[/name_u]. One of my personal favorites is [name_f]Catherine[/name_f] [name_f]Ophelia[/name_f] nn [name_f]Coco[/name_f]. 
Thanks @elenacroatia for the idea! It’s simple yet still logical. And @lainy, [name_f]Carys[/name_f] [name_f]Ophelia[/name_f] is absolutely stunning, and [name_f]Coco[/name_f] will always make me think of [name_f]Chanel[/name_f]…so naturally I’m now 100% obsessed with this idea ”
[name_f]Carys[/name_f] [name_f]Odette[/name_f] perhaps?!
[name_f]Carys[/name_f] [name_f]Ottavia[/name_f]
[name_f]Carys[/name_f] [name_f]Opaline[/name_f]/a
[name_f]Carys[/name_f] [name_f]Olympia[/name_f]