i think alot of nurseries don't do one day. they say it becuase they don't settle. i say it is because it is not worth it financially for them. dd's nursery do it but it is in north east edinburgh and has a waiting list.
My 12 month old has recently started nursery, just 2 mornings a week in Edinburgh. Similarly to yourself, there were a lot of nurseries who wouldn't accommodate this. In the end we found 3 who did and made a very easy choice between them. I think you definitely know when one feels right to you -and its nice when your instincts are confirmed to be right by the Care Commission report. The nursery is Waterfront Nursery at Telford College and they will take babies for 1 day. If the geography is right for you its worth a look. Also, have you looked at The Edinburgh Nursery and School Guide. It has a good list of nurseries and what sessions they do - although I found that in some instances it wasn't completely accurate.
Is it a particular day you need? I would have thought that some nurseries might have parents who work 4 days and take one day, I know someone who got 2 days at nursery on Monday and Friday because those were the most popular off days for other parents.