Sorption cryocoolers utilize metal hydride sorbent beds for the closed-cycle circulation of gaseous hydrogen through heat exchangers and a Joule-Thomson (J-T) expansion valve in order to achieve cold-stage temperatures below 30K. These devices have high potential for satellite missions that require long term reliability, minimal vibrations, and low operating power. Designs for nominal 25K liquid and 10K solid hydrogen refrigerators are described. Prototype hydride sorbent beds for breadboard studies of sorption cryocoolers have been fabricated and tested to simulate expected operation. The sorbents contained in the beds are VHx, LaNi5-ySnyHx, and ZrNiHx. Some of these hydride beds have been integrated with a hydrogen J-T cold-stage. These experiments confirm that the selected metal hydrides and bed designs satisfy the constraints associated with the proposed liquid and solid hydrogen cryocoolers.