Hi POL.777,
I believe that Bond Aviation in connection with Astreus offer B737 type ratings, line training and time on type. I know of a couple of people who have done this, one of which now has a full time job with another B737 operator and another is awaiting a start date with another carrier.
There are probably other carriers and training organisations but I'm not aware of who they are.
http://www.flyastraeus.com/
For Bond Aviation go to the above link and click on "Recruitment and Training" Link.
Best wishes,
Charlie Zulu.