Do you have an Auction house near you? They might need casual staff either on the day of the Auction or to organise the next auction. Small family companies may need an Admin one day a week. Museums and Galleries sometimes need gallery stewards for a few hours a week. I have seen ads in my local Town Centre for those positions.

Estate agents are busier on Saturdays and sometimes employ viewing assistants for that day only.

Have you tried job boards for part-time employees, or even done a google search for your local area mentioning one day a week? Apologies if you have already tried this.