I am Welsh and I named my daughter Carys. I understand that it derives from the word 'Caru' which means love and maybe related words like 'Cariad' meaning darling or sweetheart. In Welsh the 'a' does not have a soft pronunciation so 'Ca' is pronounced 'Ka' not 'Care' or 'Ker'. That would be spelt Cer in Welsh. The second part 'rys' is pronounced 'riss'. Y being a vowel in Welsh. The pronunciation 'rees' would be 'rhys' or 'rus' in Welsh. [noted -ed]Having been familiar with the name all my life, 46 years, I considered the name to be well established but not overly common and not sounding like an old person. However, one of my friends commented that it sounded like an old person. Probably depends if you knew an old person named Carys when growing up, which I didn't.
Ok, so as a proud bearer of the name, it is pronounced KAH-ris. Not Care-is (That's more like Cerys, which I prefer slightly) or Car-is or Ka-RIS (though that's bearable.