As I look back at my photos of the lion and lioness I'm reminded about the "tricks" for taking better photos of wild (albeit captured) animals.
Make good use of your Z-O-O-M lens.
Patience is really the key. Wait. Watch. Study. Try to learn the behaviors of the animal. Sometimes I will sit for half and hour or more just studying an animal (especially if the animal is active). Even if the animal is not active, give more than a passing glance. This lion looked like he was sleeping. I waited a few minutes and he woke up (allowing me to capture this wonderful y-a-w-n).
And then he stood up and began to explore.
One hint to note: try to visit earlier in the day. Animals tend to be more active in the morning when it is not so hot outside. By the time I reached the lions it was naptime.
This is also another good reason for considering becoming a member of your local zoo. When you become a member you are supporting your zoo. Obviously, you need to check with your local program but for most that means you can visit fee free almost every day for a year.
If you can visit again tomorrow or next week admission free it allows you to take the time you need. It also allows you to follow the lead of your own little monkeys. Some children are fascinated watching an animal for 20 minutes. Others are ready to move on after 20 seconds. If you have a membership you don't need to feel the pressure to see the whole zoo today.
For parents: you can choose one animal to focus on during your visit. Learn about that animal before your visit to the zoo. Read books about that animal. After your visit, encourage your child to draw a picture about that animal. Of course, go see other animals during your visit. But when you choose an animal to focus on it helps to make your zoo visit an educational experience. You are also more likely to see your animal active if you choose ahead of time, visit the zoo in the morning, and when you arrive go directly to that animal. Think about it: If you always follow the map and see the same animals in the same order at probably the same time of day each time they will start to look the same. Mix it up a little. This will make your visits (and zoo membership) so worthwhile.
For the amateur photographer: the zoo membership will allow you the time to really learn about the behaviors of an animal. Again, visit in the morning to try to catch the animal being more active. Choose an animal or two for that day's visit. Go directly there first thing. Don't stop to see each animal on the way -- or by the time you get there it may be naptime.
Bonus of becoming a member of your local zoo: many belong to a group that will allow you to have discounts when you travel to other zoos. Not all zoos belong but you can check with your local program.