We report the progress of an R&D project of fundamental technologies for cryocooler-cooled accelerator magnets using coated conductors funded by the Japan Science and Technology Agency under its S-Innovation Program. Its target applications include carbon cancer therapy and accelerator-driven subcritical reactor. We have been carrying out design studies of HTS magnets for spiral sector fixed-field alternating gradient accelerators to show their feasibility for the target applications and to clarify the requirements of winding technologies. A three-dimensional winding machine has been developed to fabricate a model magnet in which winding technologies required for the designed magnet are implemented. With respect to the large magnetization of coated conductors, which is one of the big concerns on their uses in accelerator magnets, the magnetic field measurements using rotating pick-up coils have been made to clarify its influence on the multipole components of the magnetic field. A method for numerical electromagnetic field analyses of coils with three-dimensional shapes has been developed to predict the influence of magnetization on the field quality of magnets.