Where can I find an aircraft's year of certification (airworthiness certificate)?
The FAA has a listing of all of the Type Certificate Data Sheets for certified aircraft. 

So the first thing you need to do is determine the manufacturer. According to Wikipedia, “The Bombardier CRJ100 and CRJ200 are a family of jet-propelled regional airliners, based upon the design of the Challenger CL-600 business jet.” So look up Bombardier on the FAA site, and then open up the models made by Bombardier. 

There are lots of CL-600 variants that all use the TYPE CERTIFICATE DATA SHEET NO. A21EA. The TCDS lists the years for each variant. The CRJ200 PF is a marketing variant of one of these, so you’ll have to do some research to find out which marketing variants match the TCDS but this should get you started.