What joint health drops are best for older cat with arthritis?

Hi Debra, if you're looking for drops specifically, and not other supplement forms, one product called ElleVet comes to mind. It is a very well-researched hemp based product that has shown benefits for cats (and dogs) with arthritis. Unlike many other products, they have actually done metabolic testing and know the actual doses that provide benefit and have performed safety studies. The product originally went through trials at Cornell University. I have seen cats and dogs benefit well from it. 

I might also mention that Dasuquin for cats (or Dasuquin Advanced, though it's only available through vets) is a very effective joint supplement. It comes in a powdered capsule form and you sprinkle the powder onto (or mix with) canned/soft food. It's made by Nutramax, another company I have high confidence in. Although it's not in a drop form, I have not yet seen a cat that refuses it and I have seen good mobility improvements in patients. I hope that helps.