My informant, who grew up in Northern California learned this fortunetelling rhyme from her late father (1922-2005), the first American child of two Irish immigrants.

“Gift,
Friend,
Foe,
Sweetheart,
Journey to go.

“The idea is that if you have a white spot on your thumbnail, you’ll receive a gift at about the point in your life when the white spot reaches the edge of your nail. Similarly with index finger nail and friend, middle finger nail and foe, ring finger nail and sweetheart and little finger nail and journey to go.”
She went on to add:
“I have yet to encounter anyone else who’s heard of it, possibly because it doesn’t seem to have any actual usefulness for fortunetelling.”

While internet research did not turn up any other versions of this song, it bears similarity to another fortunetelling folk song for children which goes:
Monday’s child is fair of face,
Tuesday’s child is full of grace,
Wednesday’s child is full of woe,
Thursday’s child has far to go,
Friday’s child is loving and giving,
Saturday’s child works hard for a living,
But the child who is born on the Sabbath Day
Is bonny and blithe and good and gay.
The “Monday’s Child” song is not as arbitrary as the fingernails, as there are both underlying and overt religious connotations- “Wednesday’s child is full of woe” could possibly be a reference to the Wednesday preceding The Last Supper, when it is believed that Judas Iscariot accepted payment to betray Jesus, and the Sabbath Day is regarded as a day of joy among Christians because it is the Lord’s Day (and because it is a commonly accepted belief that Jesus rose from the dead on Sunday).
The rest of the days seem arbitrary though, in the style of the fingernail rhyme, although the middle and index finger connotations do reflect two American traditions. Holding up the middle finger is an obscene gesture in the United States and would be reserved for “foes” while the ring finger is so named because it is the finger that wears the wedding band, thus it would be the “sweetheart” finger.

Monday’s Child is actually included in the Roud Folk Song Index with the number 19526. http://tinyurl.com/5r9kjdd