Find a solid (one without holes, that is) jar opener at the dollar store, it's flexible & big enough to do the job!
Put a plastic lid over the drain then fill a glass or cup with water to weigh it down and set on the lid. It should stay in place long enough for you to do dishes, and the water not leak out. I just did this yesterday and it worked fine.
As temporary sinkstoppers, I have used clean dishcloths, clean washcloths, clean, small towels, but only temporarily, as the water will eventually leak out. Depending on how crammed you get them in the sink drain, they could last for minutes, or hours.
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