I had toyed with said idea for an eventual TL, but having two ongoing projects (plus an upcoming third) this might take a while to get worked on:
Gonzalo Pizarro, having defeated the last remnant of royalist support in the Viceroyalty at the Battle of Huarina in October 1547, goes the whole hog and proclaims himself King of Peru (as suggested IOTL by his right hand man, Francisco de Carvajal.) Negotiations are made with the Inca redoubt of Vilcabamba to secure a princess of royal blood to become the new Queen. The Inca government, reeling from the death of Manco Inca, and nominally under the 11 year old Emperor, Sayri Tupac, agrees to provide aprinces of royal blood and relocate the court to Cusco [1], as a vassal of the new King.
Soon after, Pedro de La Gasca, royally appointed President of the Audiencia of Lima and Governor of Peru, arrives with blank pardons for the rebels who desert Pizarro and commences the march southward to defeat the pretender. Concurrently, under the advice of Paullu Inca, Sayri Tupac, establishes contacts with La Gasca and offers to switch his allegiance to the King, in return for his acknowledgement of Lord of Peru, under Spanish suzerainty. La Gasca proves evasive.
As the royal force advances south to Cusco, where Pizarro has gathered his armies, they are ambushed near the Apurimac gorge by a large Indian force under the direction of the Pizarristas. Though only a couple hundred soldiers are killed, La Gasca recognizes that he has been considerably weakened overall, and accepts Sayri Tupac’s request. In Cusco, the Inca commanders tell Pizarro that the defense of the river was unsuccessful in spite of their best efforts (still, by it they demonstrate their commitment to his cause.)
In April of 1548, at the Battle of Xaquixahuana, Pizarro’s Inca allies, and his own men, desert him and he is eventually defeated. Sayri Tupac excuses himself of the ambush at the Apurimac pass and blames it exclusively on rebellious Wanka Indians instead (enemies of the Inca, and old allies of the Pizarros since the 1530s.)
The new royal government recognizes the Inca as overlord of Peru, and the colonial age begins. Missionaries are to be given free access throughout the land, and Sayri Tupac converts to Christianity, while private Spanish property is accepted and respected in the highlands, along with the already created encomiendas. Furthermore, the Inca, as an Imperial vassal, gives the Spaniards exclusive rights to trade throughout the Empire, and allows the continuation of the Audiencia in Lima, and the Kingdom of Chile as integral parts of the Spanish Empire in Peru. In return, official control of the rest of the state is reverted back to the Inca, and Spaniards residing within it agree to abide by its laws (which are to be revised and updated.)
By the 1600’s, the government in Lima, becomes somewhat analogous to what became of Hong Kong: the point of access for Spanish goods, and the point of exit for the mining goods exploited by Spanish entrepreneurs and Inka kurakas. Doubtlessly, some individuals are to be upset by the status quo, but while Spain remains entangled in foreign wars, and the Inca are left undisturbed, theoretically this arrangement could go on for quite a while. (Until Spain declines as a world power, and other other alternative powers arise, that is.)
[1] Sayri Tupac did almost do so in 1549, until the death of his uncle Paullu Inca stopped him. Suspecting foul play on the part of the part of the Spaniards he remained in Vilcabamba until 1560.