The types allowed are shown on the relevant page on the airport website.
http://www.lcacc.org/aircraft/index.html
There is a further requirement for them to be fitted with what has become known as a "steep approach kit". I believe that the Embraer 135 that operated the Cork route for a while for jet magic was so fitted but now that this aircraft has passed to BMI it is no longer fitted so could not be used currently into LCY.
In addition to commercial airliners there are now upwards of 10 rotations a day, sometimes many more, of business jets through LCY, of which the Falcon 900 is the largest regular user. Shell Oil used to base two there (sem to have moved on recently) and there's the home-based G-LCYA as well.