If you would like to purchase a ukulele for your child these are some recommended brand and models that are of a good quality and will stay in tune. They can be found easily at most music retailers.
This is the exact model and brand that we use in class. The strings are nice and soft and it stays in tune well making it a great fit for beginners. I find this to be the best quality and best priced choice overall and highly recommend it!
This is a great uke and is a slightly more expensive option with a slightly bigger sound. The strings are a bit harder to push down which makes for a clean sound but it's a bit harder to play.