Shop the latest OiOi nappy bags in Australia. Oioi offers nappy bags, change mat clutches and stroller seat liners in trendy prints which have been tested and trialled by real parents to deliver functionality, sophistication and practicality. For over 20 years OiOi have been designing nappy bags for parents around the globe. Types of nappy bags include tote nappy bag, carry all nappy bag, backpack nappy bag and leather nappy bags.