You can soak your diamond ring in half water and half Mr. Clean. The best thing to do is use an old toothbrush to scrub below the prongs. Many people clean their jewelry but do not clean underneath were the light shines through the stone. I have never used Windex but I swear Mr. Clean does the job right.
Nothing 'gets' the soap and grease off the stone but you scrubbing it...Windex works for me (I use it daily), Mr Clean and water is recommended by jewelers as well. I've soaked my ring in Windex, nothing does the trick like soaking and scrubbing. Only use something as harsh as Windex if you have platinum as it may eventually eat away at WG or Gold.
When I saw the word "Windex" in this post, I just had to take a peak. For those of you who saw the movie "My Big Fat Greek Wedding". the father of the bride carried a bottle of Windex around with him and used it for EVERYTHING! The movie was hysterical and highly recommended!