What a wonderful idea! Fingerless mittens are usually pretty quick and you can use up your odds and ends as well. On ravelry, there are many simple and free fingerless mitts patterns.
Wendy Johnson has a simple pattern on ravelry and it is a free pattern for knitted fingerless mitts.
If you crochet, here is a pattern that seems like it work nicely.
We also have a few free downloads on the KP website for fingerless mitts that have some patterning on them if you are looking for something with a stitch pattern incorporated into the design. Click here and scroll all the way down to see the free downloads.
Hope this info helps and the best of luck in getting mitts to this great cause.
I wanted to send a message but have to be a friend in order to do so. I wanted to ask some questions regarding this. I would very much like to assist, but would also need a pattern to complete them. I've only been knitting a couple of years and not accomplished enough to figure out how to do them without a pattern. There is a dialysis clinic in my own city that would probably like them as well so could knit for both. I would need to know what kind of yarn (i.e.: DK sport, worsted, bulky, etc.), approximately how much yarn for each set, etc. Please contact me regarding this so I can start. Thank you.