The only one I know of is WOSO San Juan, Puerto Rico, which runs the NPR news show All Things Considered, and it is listed on the NPR station list at
www.npr.org. It is one of Puerto Rico's few (only?) English-language stations.
www.woso.com
In the Virgin Isles, a commercial band FM station runs NPR 24/7, but it seems to be leased by an ad hoc public radio group.
Interestingly, noncommercial stations that run religious programs, even just a few, find it difficult to become or retain NPR membership. Two cases were WSMC Chattanooga and WFUV New York. The parent Fordham University argued with CPB and NPR officials that broadcasting Sunday Mass and one or two other religious programs hardly constituted using tax-generated funds for advancing religion, and at any rate, NPR's stricture was an infringement of freedom of speech. Fordham prevailed. Both WSMC and WFUV are back as members, as is WAUS Berrien Springs, Michigan.
It seems that NPR is now a little more flexible about membership, but stations that are predominantly evangelical in purpose are not members. It is interesting that, on the other hand, NPR accepted WOSO, but under what terms I do not know. Perhaps commercial sales in the NPR block are not permitted. Puerto Rico is a special case, of course, because of language. NPR also lists WRTU San Juan, a noncommercial station owned by the University of Puerto Rico. It does not seem to be a student-oriented station, and it runs a great deal of English programming, but not the NPR news shows or even, as far as I can see, Car Talk or Prairie Home Companion. See
www.wrtu.org. Most of the site, but not all, is in Spanish, and even high school Spanish will get you through the site.