There are modern and there are vintage, circular, and flat, metal and plastic knitting machines for kids. The list below covers some of the extensive list of machines manufactured for children. However, some beginner machine knitters can use these machines too to explore whether machine knitting is for them or not.
Because these machines are made for kids (with short attention spans), most of these machines (with some exceptions, like vintage metal fat beds and Addi machines) are not of the most superb quality.
Addi Express, red plastic, circular, 22 needles, modern, bulky
Addi King Size, red plastic, circular, 46 needles, modern, bulky
Corona Junior Knitter CHJ-3, metal bed, standard-gauge, basic/manual, vintage
Genie CHJ-3, metal bed, standard-gauge, basic/manual, vintage
Hello Hobby, plastic, circular
Janome Junior Knitter CHJ-3, metal bed, standard-gauge, basic/manual, vintage
Mattel, brown, plastic, circular, 16 needles, vintage, bulky
Sentro
Sister, plastic