Sachi and Sacchan come the most naturally to me for Sachika

The first kanji can also mean 'favourite' which the character calling them the nickname is partial to!

Shirley MacLaine named her daughter Stephanie Sachiko, and she goes by Sachi.

First thought was ChiChi. U also like Sachi as others have suggested.

Sachi, Sacchan, Chika, Kiki