Advice wanted: Emailing a well established for a postdoc in their lab. (No jobs advertised)

Hi Reddit, I am turning you to advise. My current postdoc which I was basically given is soon ending. Has anyone had success approaching PIs for postdoc funding in their lab when the PI isn't actively advertising/recruiting a postdoc?

I had a very successful PhD (100+ citations first author paper) but my first postdoc didn't really get any useful results (no first author publications). This PI's research is in my field and I think I could add a lot to their research with the models I use currently.

As I've not really approached PIs previously I don't really know how to word things in an email to ensure I am seen as both professional and serious candidate worth putting funding into. I don't even know if I'm supposed to send a CV attached or if this comes across as cocky?

Figured some of you have been through this process so could advise me. Thanks in advance.