How fortunate you are to have such a treasure! Peonies are one of my favorite plants, especially the herbaceous ones.As far as ridding your garden of grass without hurting the beauties, thats a procedure that obviously will take time and care.
The very first thing I would do is to re-edge the area around the bed. My prefered method is to push straight down with a shovel on the lawn side and then dig in at an angle from the bed side, leaving a wide 6 inch deep trench. The straight cut on the lawn side makes it harder for grass to invade, and the angled side allows the mulch to fill the trench and give a nice sloped appearance to the bed. If you don't re-edge, your grass invasion will only get worse.
Ortho makes a product called Grass B Gone, that will kill common grasses but isn't supposed to harm ornamental plants. You will see some discoloration on the leaves, so I would definitely test it on a small area first to ensure the peonies won't be harmed. If you are careful not to get any overspray on the leaves, you should be safe, as this type of chemical is absorbed through the green part of a plant, and is inactive on the soil. Proceed cautiously and slowly, with such a wonderful collection of peonies. I would continue to hand dig as much as you can, and use a chemical only as a last resort on the tenacious patches that just won't go away. good luck.
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Printer-friendly view of this garden