When we have students who really struggle to build stamina, we find sand timers can really help. Students push themselves to read while the sand is running. Then they turn it over and take a quick break with a small tool that will allow them to fidget in place. Once the sand runs out, they turn the timer over again and get back to their book. It isn't uncommon for students to wean themselves off the tool as they gain longer and stronger stamina, and develop the intrinsic pleasure we want them to have when they read.
These sand timers can be found at party supply stores, but if there isn't one near you, you can purchase them from Rhode Island Novelty.