The English translation for this just seems really clumsy unnatural to me. In conversation, I would personally word it as "I work every day but Sunday".

'I work daily except Sunday' would be another option.

"I work other than on Sundays" I feel should have been accepted.

"on" is optional

Could be a good title for a priest's memoirs, depending on the meaning of the sentence. To me it meant "I don't just work on Sundays."