O.k., here's what I did: I have a list of 60 traditional songs that I know by heart (or did when I printed it! The reason for the list was to counteract that moment of blank panic when called upon for a song). I checked the list to see if I could pull out one from each of the six categories.
Hmm...
friendship -- none, though from my non-trad and non-memorized repertoire, I'd pick Judy Collins' "Open the Door"
joy -- "Rambling in the New Mown Hay"
comfort -- "All the Pretty Little Horses"
knowledge -- "Young Man Who Wouldn't Hoe Corn"
religious -- this list is thin on that point, unless the "Farmer's Curst Wife" would qualify. Though, I could easily break into "Swing Low, Sweet Chariot" or a few others, if need be! ;-D
love -- it's heavy on this end, of course, although, but from the ballad point, that is involving love, but not love songs in the lyric, first-person sense. Something like "Do You Love an Apple" might be the clearest pick here. Those ballads, they'd seem to fit the love + knowledge (as in lessons to be learned) joint category.