I Know it would probably been a bad idea for a European King to come out and say he wasn't a Christian, but are there any private letters that might support something like this?
I don't know of any born Christian rulers in medieval Europe who were secret apostates, but perhaps someone else will be able to provide examples. My inclination, however, is to say that, once Christianized, the odds of a king converting to another religion or becoming atheist is very low—as a rule, Christian kingship draws its legitimacy from the will of God, and rejecting Christianity would be akin to abdicating your right to rule. Regardless, however, there are some examples of rulers before the 11th century who unconvincingly "converted" to Christianity.
Some background: Christian kings in the Early Middle Ages, notably Charlemagne but many others as well, often considered the conversion of pagan peoples to be the prerogative of the state. When possible, kings would use conquest and forcible conversion; elsewhere, these kings used trade agreements, missions, and political alliances as pressure to convert pagans. The Christian territories, both West and East, were wealthy and militarily powerful, and so this pressure was often successful, both with rulers and lesser men.
However, many recently converted pagans were questionably serious about their new Christian faith; Robert Ferguson relates a story in which the Carolingian court sponsors a mass baptism of Vikings, and the King finds to his dismay that he is out of the traditional clean, fine white linens that he normally gives to the converts. When he has old clothing torn up to use in their place, one of the Vikings complains that after his previous twenty baptisms, he received a much nicer gift. Conversion to Christianity was, to many Germanic people, more practical than sincere. And, of course, we can at least question the sincerity of any forced conversions.
As for rulers: the same idea applies, except that the rewards were more political and social than physical (although they were often both). One of the more famous examples in the English world is Rollo, a Viking raider who in 911 agreed to convert to Christianity and defend northern France from raiders, and in exchanged received what became the Duchy of Normandy. Despite outward conversion to Christianity, according to one chronicle, he had one hundred Christians beheaded in front of him, to atone for his betrayal of the Viking gods, but still gave some a large amount of wealth to the church in his will. Conversion is a tricky matter: how Christian is someone who ritually sacrifices one hundred Christians to his old gods, but raises his children as Christians and gives to the church in his will?
Main source:
Robert Ferguson, The Vikings: A History
Fredrik II, Holy Roman Emperor, King of sicilly was excommunicated several times. He told the pope he would join the crusades and didn't. When excommunicated he went with a tiny army to Jerusalem and made a tiny kingdom there with his exceptional diplomatic skills, all without the blessings from the pope. He was called stupor mundi, the ashtonishment of the world, and invited scholars from both the islamic and christian world and was extremely interested in science and art. His harem is supposed to be vert arabic and he used muslim soldiers aswell as Christians. Om campain he is supposed to have said to a christian company as he was looking at a field of wheat: look, there grows your god.(Jesus body, bread etc.)
This is what i remember from Lars Brownworths podcast. I wrote this on a phone and would really appriciate if a historian could expand on this. Do i have the right idea here or did he show more piety ?
Well, some early medieval rulers rejected the Christianity that had been imposed upon them. For example, the Heimskringla records that Haakon Sigurdsson accepted baptism and a mission to convert Norway, which he abandoned almost immediately becoming a fierce patron of the Norse gods. Also, especially in the early Middle Ages, you had rulers who were Christian, yet adhered to beliefs proclaimed heretical. The Arian leadership of many of the post-Roman kingdoms is an instance of this. However, being a "non-believer" in the sense of an atheist was not really a live possibility at the time period, indeed barely at any time period prior to the modern age. There was simply a profoundly different understanding of the world operating and it did not admit the sort of materialist atheism that flourishes today.
I can't think of any kings who showed any signs of being non-Christian. From memory, the only thing I can think of that even comes close is some suggestions that local nobility during the Cathar heresy in southern France might have covertly adhered to Catharism. That's not exactly what you're asking for.
I don't know if you are interested in an answer from 1800s, but Milan I of Serbia (ruled 1868 to 1889) was one such ruler.
According to his close friend Čedomilj Mijatović (who was also a historian - his book on the life of Constantine XI contains the most exciting description of the fall of Constantinople I've ever read), king Milan would attend church services, but considered it "a superstition" and privately was an atheist.
Interestingly enough, after he abdicated in 1889, king Milan spent an Easter in Jerusalem and after that experience he suddenly became a believer and died as a Christian 1901.
It turns out that it's nearly impossible to determine if historical figures in Medieval and Renaissance Europe were atheists. Machiavelli is one of the strongest contenders for being an atheist, and has a relatively large amount of preserved writing to use as evidence, but it's still just not possible to know what he believed.