1. Just wind up and give it your best shot at pronouncing it in Spanish. This was President Obama's initial approach at the press conference introducing Judge Sonia Sotomayor as his nominee. You can hear it at about the 3:15 mark of this clip: soft T, trilled R, accent on the final syllable: "so toe my OR."
4. Insist publicly on an "Americanized" pronunciation. Mark Krikorian of the National Review likes this idea. His suggestion is "SO duh my er" (rhymes with Niedermayer). The problem here (besides that "SO duh mayor," as in "the mayor of New York," would be more intuitive in English) is of course that it seems xenophobic to suggest that "foreign" names be arbitrarily Americanized. After all, as Salon points out, English is a tongue that has always been willing to adopt foreign words and sounds. Why draw the line just for a certain liberal-leaning Supreme Court nominee?
5. Listen to the nominee herself and mimic. At around 12:50 and again around 13:20 in the clip above, you can hear Sotomayor herself pronouncing Sotomayor in Spanish. Why not, as a matter of etiquette, simply do your best to follow this as a guide? This seems the most obvious and correct approach, and as Lawyers, Guns and Money notes, gives the person whose name you are butchering an opportunity to tactfully ignore that fact.