Part-time scholarships are extremely rare, regardless of the field of research. This applies across the board internationally as far as I know (thought I would be interested to hear of any examples to the contrary).
Personally I see this lack of part-time scholarships as a flaw as many candidates study part time and a scholarship for those researchers would effectively buy them time to work on their research which they would then use very efficiently, even if its just a day or two per week, without them having to quit their job and other responsibilities in order to go full-time.
There are many studies showing that part-time research candidates tend to make better use of the time available. Because they have to! :-)
Some departments have a small budget for paid research but, much like teaching work, this can have its limitations as you often end up working many more hours than you are actually getting paid for. It may be good researcher development but in many cases can be bad economics.
The best solution in my experience is to keep the job you already have if you can and negotiate for a bit more flexibility and reduced hours. Its amazing what you can achieve if you can get a good routine going and use your time effectively.