TL;DR: The search terms to use may be "kidback adapter," "child stoker adapter," or "child stoker kit."
Googling for "tandem child bicycle crank" produced a link to Sheldon Brown's site, which had a page on tandems and children, and which had this to say:
For smaller children, (or larger tandems) a "kidback" attachment is needed. This consists of a "bottom bracket" that can clamp onto the seat tube of a conventional tandem, so that even a toddler can reach the pedals. Most tandem manufacturers offer kidback kits as an option, and there are also aftermarket units available from various sources.
The "bottom bracket" of a kidback is typically 1 1/2-2" forward of the seat tube, so it is best to move the stoker saddle as far forward as possible, either by reversing the saddle clamp if a "pipe" type seatpost is used, or by using one of the forward seatpost adaptors made for use with aerobars. In addition to improving the child stoker's leg angle, the forward saddle position reduces the reach to the rear handlebars.
An extra-long stoker stem is also called for with a kidback, preferably one that is adjustable for length. Many kidback users use drop type handlebars flipped over so that the child can hold onto the outside of the "drops". The U-shaped handlebars supplied with many small-wheel and children's bikes also can extend back to where the child can reach them.
A child as young as 2 1/2 can stoke a tandem with a kidback attachment, although only for relatively short rides. With time, growth and experience, your stokid will gradually be able to happily complete longer and longer rides.
A subsequent search for "kidback" showed, among others, a link to Rodriguez Bicycles, which sells tandems and these adaptors. There may be other companies selling them. This is just the first site I found, and I didn't search further. Note that per the FAQ, we strongly prefer not to make specific product recommendations. Also, kidback may have been Rodriguez's brand name, and a more general term may be "child stoker kit" or "child stoker adaptor". I would assume that many tandem manufacturers will offer these kits; Burley, when it offered tandems, seems to have done so (as described on Rodriguez Bicycles' site), Precision Tandems does (and the link goes to an installation guide), and Santana Tandems does also.
I see the question got at least one close vote, but sometimes, knowing what to Google for is not trivial, especially if you lack other specialized bicycle terminology.
The stoker adapters clamp around your stoker seat tube, and they contain a bottom bracket inside. I don't know tandem terminology, but you do run a short length of chain from the child's crank to the actual stoker crank. Below is a photo of the actual stoker crank, taken from Ray Dobbins:
In purchasing one of these, you'd need to match the clamp's diameter to your seat tube diameter. It's probably worth reminding users to adhere to torque specifications here. The Precision Tandems link above shows the possible consequences. For steel tandems, particularly with thicker tubing, I'd assume it's harder to over-torque the clamp. I'd be more careful with lightweight racing tandems. Unfortunately, I have not come across suggested torque specifications. You could start with the torque specs for seatpost clamps, probably 4-8 Nm (but check if your tandem has a different spec). Given the expected power output of a small child, something in this range should be enough to secure the clamp.
I'm not sure what lengths kids' cranks come in, but I'm sure it's safe to assume a child stoker adapter kit would come with a crankset of appropriate length. Santana Tandems (link above) gives you a 125mm crankset. An alternative is that you can purchase crank shorteners and use an adult-sized crank. I'd assume a kit would come with a length of chain, but if you're buying a second hand kit, you might need to get a chain of more appropriate length to your setup.