The best replacement for potassium iodate is potassium iodide.

The best alternatives to potassium iodate are rated as following:
★★★★★  potassium iodide
★★★★★  iodide

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Speaking about potassium iodate, one probably shouldn't forget about sodium thiosulfate.

Other search terms related to potassium iodate and their ratings are:

★★★★★ sodium thiosulfate
★★★★ potassium iodide
sodium thiosulphate
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potassium iodate
potassium iodide