If the non-profit has a known affiliate code, adding it to any random Amazon item should be sufficient.
There is also AmazonSmile, although I am not 100% sure whether affiliate links still generate revenue when using a Smile link.
Smile transfers a portion (0.5%) of the sale to a charity of the buyers choice. You can't force or even suggest one in the link and it only applies to smile.amazon.com links. I think St Jude's is the default though so they may come out ahead if you change the URL.