How can I meet a mature lady with character who desires a stable marriage?

You start by looking for someone to date, you are talking about marriage and have not even meet them. How about slowing down.

Where are you trying to meet people now?

There are many websites that you can post your story on and get prospects.

Unfortunately, this isn't one of them.

It just happens dear, be patient , quite often when you least expect it , someone amazing comes into your life... out of the blue :)