There is no English translation of the Psalms which is both in the public domain and generally approved for Catholic liturgical use.
The main problem is finding genuinely public domain texts. I agree with Adam's suggestion, but the problem is that the Coverdale has been revised many times and the revision in the AU may still be under copyright. Also it is not clear whether the BDW is licit for use outside the Anglican Use. (I suppose in the United States you could invoke the "some bishop approved it" rule, if you mean to sing them.)
The only generally accessible and unequivocally public-domain English psalms I can think of are the revision of Coverdale's in the 1662 Book of Common Prayer, the version in the King James bible, and the version in the Challoner Douay Rheims translation of the Vulgate.
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