Being overqualified as a barrier for getting a job
When they say you are overqualified, it probably means:


They are afraid that someone with a Ph. D. will demand a higher salary than they can afford to pay;
They are afraid that you will get bored with the job and quit after a few months because the work won't be challenging / intellectually stimulating for someone with a Ph. D.


So, in your cover letter, you have to tell a good story that addresses the above two items (i.e., tell them why you know you will love this job and not get bored with it). If you search around on google, you can find many articles / blog posts giving more detail.