Here is the original 19 July (Italian) article in L'Osservatore Romano. Father Z's post from yesterday quotes the CNS 22 July article.
Might be best to look for that book in the town of Carpineto Romano itself, where it was published. Does not appear to have a wide distribution.
Today I E-mailed the town the mayor, Matteo Battisti, who wrote the preface, to see how to obtain a copy.
Update: Having just perused a PDF copy of the book from editor Stefano Gelsomini (who tomorrow will send me the book) the work is much less Latin than the propaganda seems to claim. 8 of the riddles are in Latin (with Italian translation), the eighth is repeated, and the remaining 17 are only in Italian (as written by the Author). Then the book concludes with a few of the Pontiff's most famous poems in Latin. So, it is the first 8 riddles which are of Latin riddle interest, republished for the first time from the time they appeared in "Vox Urbi" under the Holy Father's pen name "X". Here is my transcription of those Latin riddles of Pope Leo.
1. Pars prior interdum velis ornatur et auro,
Altera pars prisco tempore nummus erat.
Uno iuncta simul verbo pars utraque gentem
Rapto viventem belligeramque notat.
2. Ros-mariunus
Creditur a caelo noster descendere vertex,
Pes noster medium per mare captat iter.
Sed capiti coniunge pedem; surgemus ab horto,
Dantes, quod foliis, flore et odore iuvat.
Nec verum arboribus similes, nec dicimus herbis,
Nec squama, aut pinnis res tribuenda mari.
3. Et dolet et gaudet pars prima, sed altera servat
Quo vescare; refert utraque iuncta decus.
Parte priore cibos condimus, amice, frequenter;
Enclyticam dicis reliquam. Vis utar utraque?
Obvius esto.
4. Indus-tria
Altera pars numerum designat, prima sed amnem.
Utraque iuncta animi est dos vigil atque manus.
Canis-ter
Pars prior est animal, numerum notat altera; vellem
Utraque iuncta tibi mitia poma daret.
5. Quae prior est pars, glande; pilis pars altera gaudet:
Utraque iuncta suo pondere gaudet iners.
Esse cupis primus? Postremum quaere: secundum,
Si felix, facias, litis ut aura somat.
6. Quae prima hic aderunt quod non violabile signant.
Altera, quae, o lector, tonsa retonsa geris.
Integra sunt unum, duo sunt, sunt quattuor, immo
Si tres adiicias, templa Deumque sonant.
Nasceris his, vivis, moreris, depasceris hisce;
Ecquid si tollas? Nil tibi Christus habet.
Mons me inter gemitus primum primo edidit ingens,
Et genti exiguus ridiculusque fui.
Altera Penelopis fovi sine labe pudorem;
Quid mihi? Liquerunt femina virque simul.
Coniugio hoc animal cunctis inamabile nascor,
Exosumque avibus tigride et angue magis.
7. Sanguinis et vitae fons ac effusor in artus,
Victimaque in primis irae et amoris ego.
Ad iuga montis ego sedeo pars altera summi,
Meque hinc nulla aestas, nullaque vellit hiems.
Iuncta haec verba simul tibi dant ventura cientis
Nubibus a mediis utraque nomen avis.
Me Guidus monachus genuit; genuere sed ante
Vates; in septem filia sexta fui.
Altera, quae inde sequor, sum res tua, candide lector,
Candida, nigra, rubens, cultaque crine frequens.
Mixta simul... proh! cur mixta immutamur in illud?
Nos sumus..., heu! taedet dicere, triste sinans.
8. Iosepho Lovatellio
Primum, mi Lovatelle, cum bibissem,
Phthisi convalui ocius fugata.
Cymbam, quae liquidis natabat undis,
Alterum maris in profunda mersit.
Quid totum, tibi nosse dant ocelli
Turgentes, faciesque luctuosa,
Et quae nescia comprimi aut domari
Heu matre exanimi, intimas medullas
Angit, excruciatque vis doloris.
(9-12 [9 being a repetition of 8 above] from H. T. Henry Poems Charades, Inscriptions of Pope Leo XIII 1902, are not given in Latin in Henry or in this new book, which simply reproduces the Italian of Henry [they were written in Italian by Leo himself]). The only unpublished Latin material in this book is therefore what I have provided above. Enjoy.