We plan to develop a new improved cooling system for the Superconducting Kaon Spectrometer (SKS) magnet and transfer the magnet to the K1.8 beamline of the Hadron Hall of the Japan Proton Accelerator Research Complex (J-PARC) for further use in nuclear physics experiments. To replace the present 300 W cryogenic system, we will adopt a new cooling method that uses 4 K Gifford-McMahon/Joule-Thomson (GM/JT) cryocoolers. In order to decide a practical design for the new liquid helium reservoir of the magnet, which will be equipped with GM/JT cryocoolers, cooling tests on a GM/JT cryocooler were performed from February to March 2007. We constructed a new cooling test stand with a GM/JT cryocooler and measured the cooling capacities under several thermal shield temperatures with or without a baffle, which helped prevent convection. Based on the test results, we have finally decided to adopt three GM/JT cryocoolers for the new SKS along with a baffle and an additional dedicated GM cooler to cool the thermal shield of the GM/JT ports. © 2008 American Institute of Physics.