Good news! Being playful and creative with your kids is actually a mindful thing to do.
There are an endless variety of games that develop mindfulness skills like deep breathing or emotional self-regulation. Here are three I've been using recently with preschool students. Each can be adapted for older ages, as noted.
1. Listening Button
Experiment with your - and your child's - listening button. Do this when listening is NOT a challenge, but rather can be a playful thing to explore together. Embody a person (or animal) who has trouble listening (maybe you're on a pretend phone, maybe you're pretend-listening to some music). Be challenged to listen until your child finds the 'correct' button (possible button locations: under the ear, on the nose, on your big toe). Maybe the button moves around, too. The mindful result is self-awareness and, of course, greater attention to what it really looks like and feels like to listen to someone else.
Elementary student version: Since they are quicker to get the game you can try it right away during a tense moment (rather than introducing it initially through play). Perhaps you've asked your 2nd grader three times to come to the breakfast table. Instead of yelling or threatening, get physically close and declare 'Oh! I must've forgotten to turn on your listening button this morning!' (Then push a 'button' dramatically and with a wonderful sound effect). This is certain to get their attention and move you both past the temptation of digging in your heels or turning it into a power struggle. Or: Make a listening button together with markers and a piece of paper. The listening button can randomly appear, and a child can use it on parents too!
2. Your Belly's Voice
While playing - not eating or about to eat - give your belly a voice. Let it speak its truth. Is it hungry? Empty? Achey? Quiet? Loud? Have your belly talk to your child's belly and ask it some life questions, like favorite color or book. Just give it a voice and see where it goes. The mindful result is tuning into your body and appetite. On a basic mindfulness level that's awesome. But it's also a nice communication tool for when it is meal or snack time. You can ask your belly questions about hunger levels and food choices. For picky eaters I find that this can help shift the energy away from power or rules and toward curiosity and exploration. For 'good' eaters it can provide more body awareness around hunger cues and variety in diet.
Elementary student version: Jump right into talking to your child's belly. Look it in the 'eye' and ask it what it wants to eat. Play naive and ask it to teach you about growing foods versus snack or treat foods. Or: Draw on your or your child's belly (apparently there are temporary tattoos for stomachs, pictured above). Give your belly as much personality as you would a puppet or character in a book.
3. Breathe to the Sky
Find a quieter moment and introduce a character or thing that really wants to visit a cloud (or the moon or sun). Ask your child to help out this new friend. Then you and your child lie down on your back. Show your child how to breathe in through your nose to collect the most air as possible (visualizing a balloon in your stomach) and how to breathe out through your mouth, lips pursed to focus the breath. Together you breathe in and out, blowing your friend up to the sky. Do 8-10 breaths for best engagement of the relaxation response. Create a visual story, talking to your child between breaths about the progress your friend is making -- above the trees, above the rooftops, near a cloud, next to a bird. Having clear markers makes it easier to visualize the next time you want to encourage deep breathing. The mindful result is the physical sensation of deep breathing and noting the relaxation response, as well as teaching a skill that can be used for emotional self-regulation.
Elementary student version: This doesn't need much tweaking for the older sect, just a different imagination to tap into whatever engages your child. The older kids will want to know why or need a motivation to do it. You can ask him about what he usually does when he's feeling scared or angry, and how well those strategies work. You can let him know that you like to practice this because it helps you when you're having a difficult time or need a little break. The more you can frame it in a way that is playful for them - like, a Star Wars character who might need this sort of training to become more effective in their fighting - the more motivation and engagement you'll discover. Trial and error. Not working the first time doesn't mean won't work - keep trying! This is a life skill that is as important as eating well and exercising.