In many cases “weak wrists” implies that the flexor and extensor muscles of the forearm are undertrained. I agree with Karin, not always. I like to use resistance bands (theraband or the like) to isolate, engage and resist wrist flexion and extension. Something so simple as squeezing on a tennis ball can be helpful.
Has their condition been diagnosed? Arthritis is very common in the wrist joint. The best thing for arthritis is range of motion exercises. As Karin mentioned stay away from bodyweight exercises supported on the wrists if this is painful. Pushups, for instance, or planks can be done with risers often eliminating the wrist pain. Strengthening the flexors and extensors of the hand may be helpful, but not necessarily of the forearm.
On a personal note, I think you have a great first name! Haha. In regards to your question, I hope I don’t get slaughtered on here for this, but some of the things that I’ve found helpful for developing strength in the wrists have been to take some heavy dumbbells, and just grip them and stand while holding them for about 15-30 seconds at a time. They have to be fairly heavy to get the full effect. I find that this “gripping” exercise is good for getting my wrists used to bearing heavier loads. I don’t move my wrists, I just grip the heavy weights. For clients, it would be best to get these heavy weights up off the ground to about waist level, preferably on either side of the client so he or she could simply grab one, grab the other, then drop one, drop the other without too much strain on the back or shoulders. Make sense? It’s up to you to determine if that’s appropriate for your clients.
I’ve also found that using barbell collars to strengthen my grip has proved most beneficial in increasing the tone and strength of the muscles in my forearms. I’m talking about the collars that you can grip together. I’m sure you know what I mean. The great thing about these guys is that they come in different “strengths.” The ones used on the olympic bars are stronger than the ones used for the curl bar or for the “do it yourself dumbbells.” I grab the collars in both hands and bend my arms at the elbows to bring my forearms parallel to the floor. Then while maintaining wrist integrity, I slowly grip the collars until the two ends come together or almost touch. I slowly release the grip, and I repeat that process until I feel like my muscles are sufficiently fatigued (about a minute, maybe). I’ll do a few sets of that. The great thing here is that you can do the grip as fast or as slow as you want to. Both ways will activate different fiber types. You can bend the wrist in different directions to focus on certain muscles. You can put your arms in the air and do the exercise for more fatigue, which may or may not prove beneficial in increasing the endurance of those fibers in the forearms.
Just some thoughts. I’m not saying any of this is right or wrong, I’m just speaking to what’s worked well for me.