Depends on how and what you count, yo. Do non-sonnets count?
Background (can be safely skipped)
Petrarch worked on his sequence to Laura, variously referred to as Il Canzoniere ("The Songbook"), Rerum Vulgarium Fragmenta ("Fragments of Common Things"), and Rime Sparse ("Scattered Rhymes"), throughout his poetic career. The Wikipedia entry on the sequence says:
Petrarch's meticulous dating of his manuscripts has allowed scholars to deduce that the poems were written over a period of forty years, with the earliest dating from shortly after 1327, and the latest around 1368. The transcription and ordering of the sequence itself went on until 1374, the year of the poet's death.
It's tempting to think that perhaps Liszt's numbering of the sonnets he set to music reflects some version of Petrarch that was superseded by a later ordering. However, there is no evidence for this in the manuscript tradition; none of the mss. have Poems 61, 134 and 156 ordered as Liszt numbers them, 47, 104, 123.
The earliest known manuscript of the poems is Vat. Chigi L. V. 176. The manuscript includes poems by Dante and others; Dante's Life of Bocaccio; and 215 of the 366 poems in the Canzoniere. In the introduction to his translation of Petrarch, Robert M. Durling says:
This version of Rime Sparse consists of 215 poems (1–120, "Donna mi vene," 122–156, 159–165, 169–173, 184–185, 178, 176–177, 189, 264–304; in that order).
In later manuscripts, Petrarch reordered the poems from 157–366 a fair bit, adding new poems and occasionally excising existing ones. But he made only one change to any poem from among the first 156: to replace "Donna mi vene" with a different, newly composed poem, "Or vedi, Amor". He was working on a new ordering of 336–366 when he died.
The set of poems in the sequence 1–156 in the Chigi manuscript stayed in that order through all the different versions of the Canzoniere. Since all three of Liszt's songs are from poems within that set, it's safe to assume that they weren't reordered. In that case, why does Liszt have the sonnets numbered as he does?
The answer you've been waiting for
Because the Canzoniere is not just sonnets. Alongside its 317 sonnets, it includes ballads, sestinas, canzoni/songs, and madrigals. "Benedetto sia 'l giorno" is indeed Sonetto 47 in the sequence. But it has been preceded by four ballate, two madrigali, two sestinas, and six canzoni in addition to 46 sonetti. That's fourteen poems that are not sonnets before Sonnet 47. Math is hard, as Barbie said, but let's try to add those numbers: 47 + 14 = 61. Ecco.
So yes, it all depends on what you're counting. The 47th sonnet in the sequence is "Benedetto sia 'l giorno". But that sonnet is the 61st poem in the Canzoniere. If you look through your edition of the Rerum Vulgarium Fragmenta, you can clear up the other two anomalies in the same way as well.
The information in the answer given over at Music SE to this selfsame question is misleading and/or wrong. There's nothing erroneous about either numbering, and scholars didn't reorder the poems either.
- Durling, Robert M., trans. and ed. Petrarch's Lyric Poems: The Rime Sparse and Other Lyrics. Cambridge, Mass: Harvard UP, 1976.