Stress is inversely related to the amount of control you have over your situation. The job search process can be highly stressful because so many things are out of your control:
whether a job in your field will be advertised
what the competition for that job is like
how the decision to hire is made
Those are important things. The job search is inherently stressful.
However, you can manage your stress better by focusing more on the things you can control.
Defining your goal
What do you really want in your career? I don’t mean a specific job, but rather what qualities does that job have?
Those qualities might be found in numerous careers. By identifying what is important to you and what you have to offer an employer in relation to those things, you can expand the possibilities.
Just because you can’t name other jobs that meet your criteria doesn’t mean they don’t exist. You might need to do some research. Talk to some people. Investigate what people do in different companies and what certain jobs really entail. You will need to question your assumptions and gather some facts.
Focus on tasks rather than outcomes
If the measure of your activity is securing a particular job, you are going to feel like most of what you do is futile.
You know that certain tasks improve your chances:
networking with people who work in relevant fields
gaining relevant teaching experience
writing targetted cover letters for specific jobs
Recognize your achievements in these tasks.
Stop doing low value tasks
Are you sending out applications to jobs for which you aren’t really qualified and aren’t even close? I’m thinking about jobs in your discipline that specify a field that you really have to stretch a lot to say you can teach.
Stop doing that. You are wasting everyone’s time. If hiring committees are receiving in the order of 100 applications for every academic position, the first ones to be dropped from consideration are the ones that don’t meet the basic requirements. No one is looking for a warm body with a PhD.
The time you spend putting together an application for a job you are not qualified for (and probably don’t want anyway) could be better spent doing something that will make you a better candidate for a job that you do want:
writing another article
getting the dissertation finished (if it isn’t already)
having coffee with someone who can tell you more about a job you don’t know enough about to know whether you are either qualified for it or interested in it
an internship that gives you skills and knowledge of other options
Look after yourself
Eat well. Exercise. Get enough sleep.
Your brain and your body depend on these things. You are only fooling yourself if you think you are productive without them.