You haven't stated what you are looking for, and why you can't find it. What sort of dog are you looking for? A large dog? A small dog? A dog that doesn't have needs?
If you are looking for a dog who is little maintenance and won't do anything wrong, then you probably should not have a dog. If you are simply looking for something and having trouble finding it, then just look a little longer.
One thing you could do is to foster a dog or two for an animal rescue league.There, you and your family will learn what it is to have a dog, the responsibilities, etc. This will help the dog(s) you foster and help your family, too. You will not be tied to keeping the dog, since it will eventually find a home. There is an unending source of animals needing foster, so you don't need to worry about that.
If you just cannot have a dog, explain the reasons this is so. Children need to know how life works, and the reasons things are the way they are. If you don't have time for a dog, explain this to them. Explain what dogs need, and how you can or cannot fulfill this commitment. Look it up, online for facts.
They may not immediately understand, but will eventually. If a dog does not suit your family, consider a friendly cat. It is a pet and does not require as much time, although a cat needs attention, food and litter cleaning. Hamsters and fish are also nice pets, but also need maintenance.
I also like Maxi's idea of dog training clubs. Not sure which clubs those are, and it would be excellent to know for others to find them. This is a way to have them involved, yet not have the issues associated with ownership, if you have decided that.