Kat - good for you ! I've found in playing at nursing homes (not hospices) for people in their 70's & 80's that songs popular in the 1940's & 50's go over best.
The music they danced and courted to really brings back the memories, like "Springtime in the Rockies," "Red Wing," "Golden Slippers" "Maggie," "Remember Me" "San Antonio Rose," "Faded Love," etc. Granted, "Golden Slippers" and "Maggie" are much older, but they were popular dance tunes for nearly a century. Your dad should be a gold mine of these.
One warning, the bluegrass version of "Will the Circle Be Unbroken" has some pretty somber verses - "undertaker, undertaker ... that body you are haulin'...etc."
Have fun, you're doin' people a real favor.