There was also a songbook published, with music from that production (which I saw the touring company perform back when I was in school). It had a brown folksy cover and I used to have a copy, yonks ago. You might find it on a secondhand site if you're interested.

There was an actual song called "Spoon River" which had the refrain Spoon River, Spoon River is calling me home... which I have a feeling was especially composed for the show, though there were also some well-known American folk songs incorporated in as well. Some of the cast members played instruments (I remember a guitar and possibly a banjo) and sang, as well as speaking the poems. Very well done, too.