Is your child insatiable when it comes to being lifted up in the air? Both my kids still love it although they are getting a little too big and heavy for it. To stay strong and keep up with my growing boys, I do quite a bit of upper body strength training using my own body weight (and theirs). For triceps, one of my favorites is table-top tricep dips because it doesn't require any props and I can include my children.
To intensify these simple dips, my sons (only one at a time) climb on top of me and pretends to be an airplane when I lift from the dip. I like to make him fly!
Here are two variations I do with my kids.
Standard Table-top Format: works your triceps and requires engagement of your abdominal muscles to keep the table-top form.
Note: your torso (and your child) will lower and lift as you bend and straighten your elbow. Make sure you're not lowering your body by flexing your hips more.
Single Leg Challenge: also works the glutes on both sides, and the hamstring of the supporting leg.
An alternative is to hold the single leg table-top position while squeezing your underarms and shoulder blades to activate your triceps. Try holding for 3 breathes (in and out) and then switch legs.
I love that I can do these anytime during the day and anywhere (on my kitchen floor, on a mat at home, at the playground).
Experiment and see what works for your body and your child. My sons sometimes like to lie down on my tummy for a little rest or lie back to "take flight". Other times, they like to play "London Bridge is Falling" where they try to go through the space under me as many times as they can before I fall down.
Try this several times a day (low reps) as part of play and bonding time with your child. Do it at least 3 days a week and see how you feel after a month.