Here are some other ways to say it depending on the context:
* कुमारी (koo-ma-ri) - This word literally means "young woman" and can be used as a polite way to address a princess.
* राजा की बेटी (ra-ja ki be-ti) - This means "king's daughter".
* राजकुमारी साहेबा (raj-koo-ma-ri sa-he-ba) - This is a more formal way to address a princess, adding "saheba" which signifies respect.
The best choice will depend on the specific context and your desired level of formality.