One important stress reliever to teach children of all ages that can help them deal with everything from uncomfortable feelings to tantrums, is breathing exercises. It helps them stop, relax, and refocus. This can allow them to reverse their stress response, which can feel overpowering at times, and approach problems with a clearer head. This can help them feel less stressed, and help them avoid dealing with problems in ways that will create additional stress for themselves and others.
Other strategies you can effectively teach your children include drawing pictures that express intense feelings (a precurser to journaling), talking about problems with a trusted friend or adult, playing with and caring for pets, participating in sports or other forms of exercise, and just asking for a hug when one is needed.
Also, it’s important to teach children skills like optimistic thinking, and to trust in themselves and in the world. This can promote a sense of resilience, and can help them to feel more comfortable taking calculated risks in their lives as well, handling problems proactively and reaching greater levels of success.
Finally, I think it’s important for today's parents to remember that even our children (especially our children) need some 'down time' to explore their interests and the world, to learn more about themselves, to form friendships, and to just be children. All of these things can help us do what all parents strive to do: raise children who grow into happy and healthy adults.
These are all emotion-focused coping strategies. Helping them handle stressors with solution-focused strategies like learning study skills to handle school stress, communication skills to handle relationship stress, and time management skills to handle busy schedules, can help as well.