I notice target are promoting the very cute little Fujifilm instax mini 8 camera,(its also available in other chain stores like JB HiFi and even officeworks and comes in a range of colours not just pink) which use a polaroid like style of instant picture development system. It is not digital and uses special film (which is freely available and not prohibitively expensive) to create small photos, …but almost instantly.
Most kids today will not know of the excitement of watching a polaroid develop for the first time and the thrill of getting the physical picture immediately. So there will me a period of wide eyed wonderment! However these one-off small pictures may not be what a modern kid wants since you can’t upload them to instagram, doesn’t come with a phone app etc…
So what has happened to instant photography in the digital era? Most significantly Polaroid (and Kodak) famously stopped production of their instant films. A dedicated group of enthusiast banded together, the are now called the impossible project, bought the polaroid equipment and now produce a range of film (albeit expensive, it works out at about $2 per shot), So the charm of those white bordered prints lives on, at least for some. There is a nice summary of the Status of Instant Photography in the blog post by Cameron Knight.
The other way to get an almost instant prints is to pair up your phone or digital camera via Bluetooth or WiFi to a suitable printer (not all camera and printers allow this but many of the most recent models do). The difficulty is finding a suitably portable printer and this is where polaroid are currently betting their future, they have teamed up with Pogo, which have been producing portable printers that use Zink technology (it stands for zero ink and use special paper impregnated with dye crystals that start transparent but change to colours when heated)