I just got my driver side axle and the ball joint replaced in my car yesterday and my mechanic said that my stabilizer link is loose and it's been causing a rattling noise. Is this a job that someone who is somewhat mechanically inclined can do and if so how long would it take

 

You can replace the whole end link or just replace the bushings. Depends on whats wrong with it.

It's a very easy job, both wheels must be off the ground in order to work on the sway bar. Also both sides must be disconnected or you will work against the force of the bar.