This will all be advice that you can pass to your manager, since you don't seem to have problems yourself.
To quote Bobby McFerrin: "In every life we have some trouble. But when you worry you make it double. " Stress is mostly something that you create yourself. I assume your previous manager was not that stressed, so it's not the job, it's the attitude to the job that is the problem.
What can you do about stress: A good technique is passing the buck on, preferably higher. There's a deadline, and you are sure you can't make it? And you are totally worried about it and stressed out? Tell your boss that you are not going to make it. Now it's not your problem anymore, it's your bosses problem.
A very good technique is "just say no". A lot of stress is self inflicted by saying "yes" to requests for work when you know or should know it's too much to handle. By saying "no" all these worries and stress go away. (I once worked under a manager who said "yes" to everything, regularly promised to deliver all ten items he was asked to do, and delivered only three. Bad reputation and stress for him. The manager changed. The new manager said "you can have two of these ten items, and three if the guys work really hard and we are lucky". Delivered the same three items, and everybody was happy with him, and no stress).
Another good technique is "I don't care". It's not the problems or the work that cause stress, it's the fact that you worry about them and let them stress you. If you don't care, don't worry, don't stress, then suddenly you find that with all the energy you wasted on worrying and stressing being used to find solutions instead, suddenly you can solve problems a lot easier. So instead of worrying about 101 problems, your manager should say "I don't care about these problems", and with that said pick up the first problem, handle it without caring that there are 100 more, then pick up the second problem, handle it without caring that there are 99 more, and so on.
Ok, advice for you: Make sure he figures out how to avoid stress. Until then, don't add to it because you only make things worse.