If you google cal hypo tablets it will pull up some sites that sell them. Cal hypo tablets do not contain CYA, but the do contain calcium and will raise your calcium level. If your water is naturally low in calcium that may not be a problem. If there are no water restrictions in place where you live you can drain and refill if the calcium becomes problematic.
In order to get chlorine in a solid form you will be adding something to your pool that you don't want or need its either CYA or calcium. Liquid chlorine or bleach only results in a trace amount of salt. The only pure chlorine is in gaseous form and only huge pool complexes and water treatment facilities use chlorine gas. Of course there is always the salt pool option where a SWG breaks down the salt to release free chlorine then its recombined back into salt in the pool water leaving no additional chemicals in the pool.