Formal:
* Crown colony: This term emphasizes the direct rule of the monarch.
* Proprietary colony: This term emphasizes the granting of land to a proprietor by the monarch, who then ruled the colony.
* Royal domain: This emphasizes the colony's direct connection to the monarch.
Informal:
* Colony under the Crown: This is a less formal way of saying "royal colony".
* King's/Queen's colony: This highlights the specific monarch in power.
* British colony: This emphasizes the national origin of the ruling power.
Ultimately, the best word to use depends on the specific context and your desired level of formality.