When the Disorder dialog box does not allow the option to have the governor automatically assign an entertainer... you know what that means... it means assigning an entertainer will cause starvation. The governor does not want to take responsibility for that. It's up to you if you want to cause starvation.
At the point where making another citizen into an entertainer will remove work from a food tile, the Disorder dialog box does not include the "Give them some entertainment" option. Your only two choices are to ignore it (and probably let the rioters wreck some stuff), or else "Zoom to city."
What happens when you zoom to city? You select one worked tile to make an entertainer. At this point all the worked tiles will be foody tiles. You try to select the one that loses the least amount of food (or the least amount of shields, or money...). But no matter what you choose, you will cause starvation.
One other expedient, instead of reassigning a tile to entertainer, is to move up the Smiley Face slider a notch. This will cause loss of money, of course, and force you to either slow down your tech research, or else run a deficit.
In fact, moving up the Smiley Face one notch may not be enough. You can see in the Domestic Advisor screen if the frowning faces still outnumber the happy citizens. You may need to move up the slider two or three notches to cure Disorder. Then you'll really be out a lot of money and be forced to cut down the tech research before you break the bank.
Such are the unfortunate choices we sometimes have to make: either lose a lot of money, or else starve a citizen to death. Usually it's war weariness that causes such severe unhappiness. Other things you might do, that may not be immediately possible, are: 1) End the war; 2) Capture an enemy city that has a luxury you didn't already have, already roaded and connected to your trade network, and then end the war; 3) trade for another luxury.
Make sure the unhappy city has its Temple, Cathedral, Marketplace, and Police Station once you get it back under control. Other long-term strategies would be to get Wonders that increase happiness. But when your immediate problem is to end Disorder in a single turn, there may be nothing but unpleasant choices available to you.