1. Keep it Short
Don't keep your kid out for more than 1.5 or 2 hours if she can't handle it; she'll only grow to hate it. Gauge what you know about your child, and their age, and keep them out for just enough time for them to enjoy it.
2. Bring Extra Nets
Bring a few extra nets, and when your child tires of fishing, dub them your "official netter" and let them help you with your catch---they'll feel more involved and excited that way.
3. Keep it Simple
Fish for bluegills on bobbers, not muskies on the fly. Keep it simple so they can have fun, not be confused. If your kid is getting older, begin to make it harder and harder, but not right away.
4. Choose the Right Rod
Give them a rod they can actually use. Be it a Tenkara or a spinning rod with a closed reel, make sure they'll be able to cast it on their own after a little lesson with mom or dad.
5. Choose the Right Clothing Accessories
Get your kid a pair of polarized glasses (you can get a pair for less than $20 for them) so s/he can actually see the water and what they're doing. Also, make sure to give them a well fitted life jacket, and comfy clothes they won't get frustrated wearing.
6. Snacks, Water, and More Snacks
The best distraction for kids in nearly any situation is food, so make sure you bring a lot of it, and a lot of things they like. If they start to get cranky before you call it a day, you can treat them to a snack or two to improve their mood. Once their mood is happy, they'll be wanting to catch some more little fish.
7. Do Your Research Ahead of Time
Don't go fishing if the weather isn't gonna be good. If its too hot, cold, windy or rainy, they're gonna be miserable. I know this is obvious, but still, your kid isn't gonna want to go fishing again if they're miserable because of the weather. On the same thread, check the fishing reports for the area you're heading to before you go. If the fish aren't biting, don't bother.
8. Pack extras
This is a given with children around, but bring extras. Of everything. If your little one drops something over board that means you both can't fish anymore, no one is going to be happy, and fishing might be spoiled for them for a long time. So, plan ahead, and bring extras.
9. Floating Lures and Bobbers
If your child can see the action on the bobber or lure themselves, they're gonna be much more excited to hook and reel in a fish. Otherwise, they're gonna feel like they're just staring at water.
One bonus tip: try a pond with a playground in it; take breaks here if you need to, or make sure you let them play before heading home so they leave the water with a good memory in mind, regardless of weather or not they caught any fish!