Designing toys involves a lot of creativity, so the primary stressor for toy designers is the need to continually channel those creative ideas into successful products. Designers who work for toy manufacturers are paid a salary, meaning they'll need to earn the company money by continually designing toys that sell.
It's all good when you have twenty different ideas for gizmos and gadgets, but when that fount runs dry, or if the toys don't sell as well as expected, the pressure goes up very quickly.
Stress can also come in the form of performance anxiety if you're the type to become flustered when speaking to a group of representatives from the company. You're trying to convince them your idea will sell because it's fun, safe, and will appeal to children and parents.
It's hard to convince anyone of that, though, if you're shaking in your shoes and stammering through your sentences. Those afraid of public speaking need not apply.
Independent toy designers may have even more stress, in that they're totally invested in their ideas. When they design a toy, they have to pay the costs of creating the prototype, and failure to sell the finished product might mean losing all of that investment.