The best replacement for quoting is paraphrasing.

The best alternatives to quoting are rated as following:
★★★★★  paraphrasing
★★  italicizing
★  italicizing titles
  underlining
  paraphrasing apa
  paraphrase

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Speaking about quoting, one probably shouldn't forget about citing.

Other search terms related to quoting and their ratings are:
★★★★★ citing
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Google Trends

Scale is based on the average worldwide traffic of quoting in all years. Click on graph for more.
quoting
paraphrasing
italicizing