astonsmummy, this is really a job for a monumental mason of which I was one many years ago. If you supply me with more information I will be able to advise you on cleaning it. I need to know what it is made of, a photo would be a great help!! in 1959 most grave stones were made from either Granite, Marble or Portland stone, Marble would only have been white on a grave stone, Granite would have been grey black speckles, Portland is a far softer stone usually grey and the lettering would probably have deteriorated quite a bit by now.
Is the lettering incised (carved into the stone) or raised lead (stands proud of stone)
You will need to ask the whoever maintains the graveyard or cemetery about planting a rose, basically, if it would prevent them mowing the grave with a lawnmower they probably will not allow it, worth asking though.
If you can give me some more info about the gravestone I will be able to help, especially a pic would help!!