If your child has been pestering you about getting a pet, and you can't get a cat or a dog, you might be a bit stressed out. The best solution for this is to get an aquarium-based pet (turtle, fish, reptile, snake).
Here are two different options to consider. With each one, you will need to get an adequately sized aquarium. These big glass tanks are going to be the whole world for your pet, so it's important that you get a nice one and also one that is the proper size. Once you have an idea as to what pet you would like, you can speak with the aquarium salesperson about what size (how many gallons) would be appropriate for that animal.
If you're a bit iffy about having a snake in your home, and you don't like the idea of having to deal with water filtration systems, heating systems, and balancing pH levels, like you will with a fish, then a tortoise is a good choice. These beautiful tortoises are native to a dry region of the world so their aquarium is going to be mostly dry. But dry does not mean desert-like. There does need to be a pool of water somewhere in the space for them to wade into, not just to drink from. They don't live in water, but they do need to be able to access it.
Also, the aquarium should have humidity. Don't make the mistake in thinking that because they come from dry regions of the world that they can live in a bone dry tank. In the wild, these tortoises will find lakes and river beds and burrow deep into the earth nearby to find dampness and moisture to lay in. Because they like to dig, you should give them a nice amount of substrate to play around in.
Finally, when choosing a big glass aquarium, see if you can get one that has small designs around the bottom. This will be a visual indication for the tortoise that will let them know there is a barrier. Otherwise the tortoise might end up banging into the glass. You can also get little stickers and place them on the outside, facing in. These will serve the same purpose.
If you do like the idea of fish but have bad memories of getting goldfish as a kid yourself, then consider betta fish. These are also sometimes called fighting fish. That name comes from the fact that two males will fight if enclosed together. So, you won't be putting two male betta fish together.
These fish are particularly popular because they are so hardy. Some people don't even bother heating or filtering the tank. They originally come from the rice paddies of east Asia. They are incredibly strong and can withstand varying degrees in temperature. However, this does not mean that you should just get a big aquarium, fill it with water, and dump in the betta. That's what causes them to get sick. Yes, they are strong, but you should try and create a good environment for them.
That means a filtration system and a heating lamp. You want to make sure that the water is kept clean and the water is warm. The perfect range of temperature for your betta fish is 76 to 82 degrees F. So get a heater for your aquarium and set it up so that your betta fish will have a happy, long life.
Visit a specialty pet supply store to learn more about aquarium installation and alternative pets.