Hiya, have been thinking hard on this. I come across a lot of job titles/responsibilities & project campaigns that on the surface would appear flexible enough to help manage part time considerations .. could be hugely wrong though !
Library & Children information services may have a notice board you can check for suitable positions.
Administation, advisory and consultancy.
Mobile services, craft, creche, library - book & toy.
GPs Surgery, Health & clinic possibly have afternoon clubs that require a leader or playworker (check qualifications).
Fundraising or Liason officers, voluntary work may also play a part in this.
Hospital drivers maybe, local Arts groups !?
Do you have any links to your development officer or EYs dept that could help with their knowledge.. or possibly your county.gov website has a part time jobs page ?
You can see the sort of thing I mean from this excellent page of South Leeds Health & community projects: -
www.slhfa.org.uk/PAGES/Projects.htm it's just knowing how to hear about the openings & job criteria !
Let us know what you find out
xx