I need to cut a circular hole in a joist to run a vent for my bathroom exhaust fan. I believe the joist is a 2x9 and the vent is 4inch. Leaving more than 50%. Will that pass inspection in NJ?

No - it won't pass. The rule is that you can not make a hole larger than 1/3 the height of the joist, So you are limited to 3" diameter max (assuming the true height of the joist is indeed 9"), and the hole must be centered (not near either the top or bottom edge). One solution is to apply "sister" joists on either side like in the photo below, but to pass inspection you'll need to show calculations from a structural engineer that verify it's OK.

Never heard of a 2X9 but even with a 2X10 you are over the limit. Sistering works well as shown by ebaines-Great picture!!