Inflation was understood as a result of sixfold price increases over three generations, because of the gold of the New World, and the reopening of trade with the East.
One caveat on the inevitability of inflation once the New World loot hits Europe is that IF the demand for gold and silver coins could be increased to meet the torrent of supply, inflation would be reduced or eliminated.
Given the time and place (late Medieval/early Renaissance Western Europe), one could envision an increase demand for coinage by increasing participation in the cash economy. I am not sure when the peasantry of Europe had 100% participation in the cash economy (as opposed to the manorial economy and barter), but I would think Spain of 1560 still had a significant portion of the population not using coins for the majority of their transactions. (Medieval serfs could go for months or years without ever touching significant coinage, every transaction involving direct trades of goods and labor.)
So.... if the Crown promoted elevation of serfs, indentured servants, and others not receiving cash wages (e.g. the lower ranks of the clergy) into the wage earning class, a portion of the New World coinage could be absorbed into their pocket change and sock-under-the-mattress savings, and reduce inflation.
This, and other measures to improve Spain's infrastructure, would be promoted as a means of improving the means of Christians to serve God and the Church. Cleaner, healthier, literate parishioners with coins in their pockets are better able to do God's work and support the local parish, yes? And as was the case in 19th century America, public education could be sold to the establishment as a means of converting the heathen to good Christian citizens (converted Moors and Jews in the case of 16th century Catholic Spain, Catholic and Jewish immigrants in the case of 19th century Protestant America).
Doubt any combination would eliminate inflation though. Way too much easy gold and silver coming in from the New World to drop the macroeconomic effect to zero.