I would like to include an expert Q and A system into my site that works like stackoverflow but also gives the user the option to promise money for the answer.
OSQA is an excellent Q&A that you may consider. I'm not sure wheather it has bulit-in capability to 'pay for answers'. However since it based on Django framework, you can extend and add features if you are familiar with Django.
Q&A - It's a Wordpress plugin: http://wordpress.org/extend/plugins/qa/