Many arm chair caddies attach by draping them over the arm of the sofa. If the material with which it is made is slippery, the caddy might not stay In place. Look for one that attaches with Velcro or some other secure method.
Another way for you to attach some of them is to use the coated and bendable piece of wire that comes with it. Others have ends that are long enough to tuck under a cushion. There are other ways of attachment for items in this category. Ask your seller or read online reviews.