If a Jewish king went evil (as many did), would a religious Jew be allowed to rebel against him to try to remove him from power?
Is there any condition where a king can be removed from power (coma/senility)?
It seems from the Aruch Hashulchan Haatid 71:15 that a king can lose his postion if he doesnt follow in the ways of the Torah see 14 as well.Especially if its from a Malachei Yisrael(other tribes as opposed to the kings of Dovid Hamelech). This is concerning linage ,but it seems from his,wording that even that king is not teally considered a king unless he does all which is mentioned earlier in 14 (a Navi appointed him and he follows the way of the Torah then he is called a king).
When Rechav'am (son of Shlomo) became king, Yerav'am did not revolt until after he was commanded by a navi. We also see that Yoash was assassinated by his servants Melachim II 12:21-22 when he turned bad and his son crowned in his place. Yoash himself became king when עֲתַלְיָה murdered her grandchildren and tried to eliminate the House of David and the revolt overthrew her.
These are the only times this happened in Judah. When עֲזַרְיָה בֶן אֲמַצְיָה got צרעת and could no longer be king, his son יוֹתָם refused to take the crown until after his father died and acted as regent. Melachim II 15:5
We see that Menashe son of Chizkiya was not overthrown even though he was evil and started the chain of events that ended with the destruction of the temple and the kingdom. This was even though there were meviim who could have commanded the people to overthrow him.
This would imply that the answer to your question would be no.