And as much as I love automating my own financial life, one reason sites like Tykoon haven’t quite set the world on fire yet may be that plenty of parents want to keep their children away from screens if the real-world alternative, like a jar, is a reasonable one.

“I’m not trying to win a battle for screen time,” Mr. Bruinooge said. “I’m trying to create a utility. The most time one would spend on the site is to see what’s in the Tykoon store.”

That’s a fair point, though the toolishness of Version 1 of the site is what gives a few other experts pause. Sara Fenske Bahat, a former banker and regulator who is working on a technology start-up related to families and money, worried that Tykoon felt more like a task management site than a money site. “I realize you have to start somewhere and that it makes sense to begin with the parents,” she said. “But to me, it’s like TurboTax. It’s very spreadsheet-y.” A new version of the site should fix some of this.

Neale Godfrey, the author of the classic children-and-money book “Money Doesn’t Grow on Trees,” wondered why Tykoon didn’t take more of a gamelike approach. “A typical kid is out there playing Angry Birds,” she said. “So how do you get the eyeball of that child as a parent and say to them that ‘This is what I want you to do?’ ”

Ms. Godfrey has her own answer to the question, an app coming out next month called Green$treets: Unleash the Loot, that is intended to both entertain children and teach them about money while connecting parents and other grown-ups to the endeavor. It’s aimed at 5- to 8-year-olds. “I went with the little ones, because the older ones are an impossible group,” she said.

Mr. Bruinooge said that Tykoon was already planning on bringing in some game-design talent to help make the experience more engaging. To pay for it, he’s exploring business models beyond the small payment Tykoon gets as an Amazon affiliate.

One likely possibility is to partner with major banks that would pay to offer their own versions of Tykoon, something that FamZoo is already doing with credit unions. Tykoon’s founders and their investors have tentacles into many of the biggest for-profit banking institutions, and partnering with any one of them, if it happens, could put the site squarely in front of untold numbers of parents.