It is easy to list modern rulers who used the title of King of Italy.
The kings of the modern Kingdom of Italy were Victor Emmanuel II 1861-1878, Umberto I 1878-1900, Victor Emmanuel III 1900-1946, and Umberto II 1946.
Napoleon I Bonaparte created a Kingdom of Italy and reigned as "by the grace of God and the Constitutions, Emperor of the French and King of Italy" from 1805 to 1814.
But Wikpedia has an article "King of Italy": https://en.wikipedia.org/wiki/King_of_Italy#Full_title_21
That article has a list of rulers who it says used the Latin title of Rex Italiae or "King of Italy" in Late Antiquity, Medieval, and Early Modern eras.
It begins with Odoacer 476-493, and continues with nine Ostrogothic rulers from 493 to 5553, and continues with the twenty three Lombard rulers from 568-774.
Charlemagne conquered the Lombards in 774 and added the title of "King of the Lombards" to his title. Charlemagne is followed by eight Carolingian kings of Italy to Charles III in 887. There were several kings of various dynasties - often 2 or more rivals at the same time, until 961.
Otto the Great, King of the East Franks or of Germany, was crowned King of Italy in 951 and again in 961, and was crowned Emperor of the Romans in 962, thus founding the Holy Roman Empire. The Kingships of Germany and Italy were united with the Emperorship from 962, and with the Kingship of Arles or Burgundy from 1032.
It seems improbable that the Holy Roman Emperors used the title of King of Italy often. The Ottonian Emperors used the title of imperator augustus or Romanorum imperator augustus, "emperor" or "emperor of the Romans". And so did the Salian emperors.
Emperor Frederick I claimed to be king of Arles or Burgundy from 1152 and was crowned king of Italy in 1155 and crowned king of Arles in 1178.
In a document from April 1180, Frederick used the title of:
Fridericus divina favente clementia Romanorum imperator augustus
And in a document from May, 1189:
Fridericus dei gratia Romanorum imperator et semper augustus
And that was the pattern for the Holy Roman Emperors, they mostly used the title of "Emperor of the Romans and always Emperor", and almost never used the title of king of any of the three kingdoms that were attached to the emperorship either before or after coronation as king of one of those three kingdoms.
Being the Emperor meant being the rightful ruler of EVERYWHERE so the emperors probably didn't think there was any need to list titles of various territories they ruled.
in 1194 Emperor Henry VI conquered the Kingdom of Sicily and was crowned King. He adopted the title of:
Henricus sextus divina favente clementia romanorum imperator, Rex Sicilie et semper Augustus
"Emperor of the Romans, King of Sicily, and always emperor".
The first emperor to add titles lower than king to his title was apparently Sigismund:
Nos Sigismundus dei gracia Romanorum Rex semper Augustus ac Hungarie, Dalmacie, Croacie, Rame, Seruie, Gallicie, Lodomerie, Comanie, Bulgarieque Rex, Marchio Brandenburgensis nec non Bohemie et Lucenburgensis heres
"King of the Romans and always Emperor, King of Hungary, Dalmatia, Croatia, Rama, Serbia, Galicia, Lodomeria, Cumania and Bulgaria, Margrave of Brandenburg, heir of Bohemia and Luxemburg".
It was not until 1508 that it became usual for emperors to put "King of Germany" in their list of titles, and they continued to usually omit "king of Italy" and "King of Burgundy".
So what titles were used by rulers from 476 to 962 that are listed as "Kings of Italy" in the Wikipedia article?
There are basically there different types of titles a monarch can use.
1) A plain, bare title stating their rank and position. A king could simply call himself Rex, "King", in his title, for example, without specifying who or where he ruled.
2) An ethnic title, stating what group of people he ruled (like King of the Italians, for example).
3) a territorial title, stating what region he ruled (like King of Italy for example).
During the Dark Ages and early middle ages western European rulers usually used ethnic titles.
The Anglo-Saxon kings of England from 927 to 1066 often used strange and fanciful titles but their most common title was Rex Anglorum, "King of the Angles", or "King of the English". And this was continued by the Norman kings until the reign of of Henry II (1154-1189) the first Plantagenet King.
Henry II called himself "by the grace of God, King of England, Duke of Normandy, Aquitaine, Count of Anjou".
Henricus, Dei gratia rex Angliae, dux Normaniae et Aquitaniae, comes Andegavensis
The early Frankish kings in Gaul called themselves "Kings of the Franks".
For example Childebert I in 515:
Childebertus rex Francorum
Kings of the West Franks from 843 to 916 used the simple title of "King".
Charles the Bald, 844:
Karolus Dei gratia rex
The title of King of the Franks continued to be used at lest as late as 1573 in Latin versions:
Carolus, Dei gratia Francorum Rex
The title of "King of France" was used as early as 1223 in Latin:
Ludovicus, Dei gratia Francie rex
And as early as 1308 in French:
Philippe, par la grace de Dieu Roys de France
An inscription found at Chichester in 1723 has the following inscription:
[N]EPTVNO·ET·MINERVAE TEMPLVM [PR]O·SALVTE·DO[MVS]·DIVINA[E] [EX]·AVCTORITAT[E·TI]·CLAVD· [CO]GIDVBNI·R[EG·MA]GNI·BRIT·5 [COLE]GIVM·FABROR·ET[·Q]VI·IN·E[O] [SVNT]·D·S·D·DONANTE·AREAM [...]ENTE PVDENTINI·FIL
to Neptune and Minerva, for the welfare of the Divine Temple, by the authority of Tiberius Claudius Cogidubnus, great king of the Britons, the guild of smiths and those in it gave this temple at their own expense ...ens, son of Pudentinus, presented the forecourt.
So in the 1st century AD a client king in Britain used the title of "great king of the Britons" which is an ethnic and not a territorial title.
So I have to wonder what is the evidence of the use of the title Rex Italiae in late antquity and early medieval times?
Wikipedia says that Odoacar was proclaimed king of Italy.
But the source that it uses, J.B. Bury, History of the Later Roman Empire, volume 1, page 406 says:
The soldiers had proclaimed Odovacar king.76
And note 76 says:
76 He is styled rex Herulorum in Cons. Ital. (Chron. Min. I p313, cp. p309).
There is a difference between Rex Herulorum, "King of the Heruls" and Rex Italiae "King of Italy".
So I ask for evidence of the use of the title of "King of Italy" by Odoacer, by the Ostrogothic rulers, or by the Lombard rulers.