The best replacement for cover letters is resumes.

The best alternatives to cover letters are rated as following:
★★★★★  resumes
★★★★★  letters of interest
★★★  letters of application
★★★  application letters

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Speaking about cover letters, one probably shouldn't forget about resumes.

Other search terms related to cover letters and their ratings are:
★★★★★ resumes
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cover letters
resumes
letters of interest