I haven't seen many sampler designs celebrating the 40th anniversary of Elizabeth II's coronation in 1953. This was worked in 1993 and is, unusually, embroidery rather than cross-stitch. The vast majority of later twentieth century examples of patriotic samplers are cross-stitch. The majority of the ones that are embroidery originated with the Royal School of Needlework, but I have no information to make this connection beyond guesswork.
This one is 15inches x 13inches, worked on Irish linen.
The quote says:
There is no magic formula that will transform sorrow into happiness, intolerance into compassion or war into peace, but inspiration can change human behaviour.
Queen Elizabeth II
The other sampler I've seen featuring her words is this one using part of her first Christmas message as Queen. I have seen a couple of George VI samplers quoting him. It was, after all, radio and television that made monarchs' voices heard.
As ever, if you know more than I do, which is very likely, it would be great if you'd leave a comment to add to this entry.