The best replacement for chanting is singing.

The best alternatives to chanting are rated as following:
★★★★★  singing
★★★  praying

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Speaking about chanting, one probably shouldn't forget about yoga.

Other search terms related to chanting and their ratings are:
★★★★★ yoga
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Google Trends

Scale is based on the average worldwide traffic of chanting in all years. Click on graph for more.
chanting
singing
praying