"Shiver In the Pines" mentions 5 songs:
  - Cuckoo Waltz - p. 48
  - In the Pines - pp. 49, 57
  - Pretty Fair Maid - p. 64
  - Willie From the Western States - p. 64
  - I Dreamed Last Night Of My True Love - p. 64

Cuckoo Waltz

"Choose your partner as you go,
Choose your partner as you go."---

"Fare thee well, my charming gal,
Fare thee well, I'm gone!
Fare thee well, my charming gal,
With golden slippers on!"

This text matches almost exactly with a version of Cuckoo Waltz collected in Indiana by Miss E. F. Laud. The song has been discussed a pretty good deal on Mudcat, but its Fresno State entry is rather lacking. It's one of the less-researched songs I've been able to identify from the book.

In the Pines

Where were they, where were they,
On that gone and vanished day
When they shoveled for their treasure of gold?
In the pines, in the pines,
Where the sun never shines,
And I shiver when the wind blows cold...."

Here, the song is obviously the classic mournful lament In the Pines, though the lyrics have been localized for the song here. At least, that's my assumption, since I can't find any verses matching these.

The last three songs were only mentioned in passing. Pretty Fair Maid is a well-known ballad dating back to early in the 19th century, while I Dreamed Last Night of My One True Love (also known as Locks and Bolts) dates as early as the later half of that century. Both have been extensively studied. The song identified as Willie From the Western States is probably a variant of Barbara Allen. You can see a version collected in Beech Mountain, NC (bearing in mind that Wellman was close friends with North Carolinian folk song collector Bascom Lamar Lunsford, as well as being a Chapel Hill resident himself) which you can read here.