[name_f]Coco[/name_f] definitely works and so does [name_f]CeCe[/name_f]. You can always use a C name in the middle too making [name_f]CeCe[/name_f] a very obvious nickname!
[name_f]Caroline[/name_f] [name_f]Chloe[/name_f]
[name_f]Caroline[/name_f] [name_f]Cassia[/name_f]
[name_f]Caroline[/name_f] [name_f]Cecilia[/name_f]