I find it difficult for medical reasons to generate the spit needed to do a genealogy DNA test. What are my options?
There are DNA testing companies that use cheek swabs rather than saliva for DNA tests: FamilyTreeDNA and MyHeritage are the two largest of these.
If, on the other hand, you already have a kit (e.g.) from Ancestry that requires saliva, Ancestry say:
Difficulty producing enough saliva?
If you can’t produce enough saliva in one try, refrigerate your tube in an upright position between attempts. You can refrigerate your sample for up to a week before needing to add it to the blue solution in the saliva tube.
There is also a suggested solution here but I've no experience of it so can't say whether it will work or not.