I use Windex to clean my fiancé's ring, it works like a hot damn. I don't think there is any problem doing so as it should only remove the oil and dirt and not react with Gold, Platinum or Diamond. It is also mentioned as a cleaning method on some jeweler's websites.
Quick Method: Spray or dip your diamond in Windex, rinse with water and dry with a lint free cloth.
Just for fun I contacted the SC Johnson Consumer Resource Center about cleaning jewelry with Windex:
Question: Does windex react with gold, platinum or diamonds. Some jewelers recommend
using Windex for cleaning but I just want to make sure it is safe to do so.
Answer: We have not tested and therefore cannot recommend the use of any WINDEX
product on jewelry.
I still love the stuff to clean jewelry but if your ring turns green or starts bubbling don't blame them.