Remember Pope Day? Lovely and peaceful ride in that day.
At the moment Grange Road is lovely and peaceful simply due to being blocked off at the eastern extremity to have new gas installed. Recently when they were re-roughening-up the surface of Jock's Lodge and access to Willowbrae Road was restricted from a couple of directions it too was much more pleasant for the first stretch. A few careful closures in a few places to stop things which are usually through-routes being used thereas could work wonders.
The Sunday thing is possibly just that more journeys might be seen as optional on Sundays, whereas at every other time every motorised journey is absolutely vital and must be undertaken as swiftly as machinely possible. Slightly problematic is that Sunday is Park All Over the Meadows and on Melville Drive Day; I know that it's quite possible to walk from at least the edge of the Meadows to the middle but many seem not to.
Whilst it might take regularity for habitual drivers to get used to particular roads being shut on particular days and to not gripe about it so much, a sort of rotating main-road-closure system would allow lots of little shoppy-clumps to have a go at being nice and pedestrian-friendly. Raeburn Place one weekend, then Morningside Road/Bruntsfield place, then Nicolson/Clerk St, then Broughton Street and so on.