Adam Clarke on 2 Kings 11:5

That enter in on the Sabbath - It appears that Jehoiada chose the Sabbath day to proclaim the young king, because as that was a day of public concourse, the gathering together of the people who were in this secret would not be noticed; and it is likely that they all came unarmed, and were supplied by Jehoiada with the spears and shields which David had laid up in the temple, 2Kgs 11:10.

The priests and Levites were divided into twenty-four classes by David, and each served a week by turns in the temple, and it was on the Sabbath that they began the weekly service, all this favored Jehoiada's design.