To be clear, the Church Fathers were specifically against rebellion. This being said however, some Church Fathers have in fact rather bluntly suggested that the affairs of the state and the power struggle involved in such activity is often times contrary to the Christian faith.
Tertullian
-I owe no duty to forum, campaign, or senate. I stay awake for no public function. I make no effort to occupy a platform. I am no office seeker. I have no desire to smell out political corruption. I shun the voter’s booth, the juryman’s bench. I break no laws and push no lawsuits; I will not serve as a magistrate or judge. I refuse to do military service. I desire to rule over no one – I have withdrawn from worldly politics! Now my only politics is spiritual – how that I might be anxious for nothing except to root out all worldly anxieties and care.
-In us, all ardor in the pursuit of glory and honor is dead. So we have no pressing inducement to take part in your public meetings. Nor is there anything more entirely foreign to us than affairs of state.
-All the powers and dignities of this world are not only alien to, but are enemies of God. Through them, punishments have been determined against God’s servants. Through them, too, penalties prepared for the impious are ignored.
Origen
-We are to scorn trying to ingratiate ourselves with kings or any other men – not only if their favor is to be won by murderers, licentiousness, or deeds of cruelty – but even if it involves impiety towards God, or any servile expressions of flattery and fawning.
-Celsus also urges us to “take office in the government of the country, if that is required for the maintenance of the laws and the support of religion.” But we recognise in each state the existence of another national organization founded by the Word of God, and we exhort those who are mighty in word and of blameless life to rule over Churches. Those who are ambitious of ruling we reject; but we constrain those who, through excess of modesty, are not easily induced to take a public charge in the Church of God. And those who rule over us well are under the constraining influence of the great King, whom we believe to be the Son of God, God the Word. And if those who govern in the Church, and are called rulers of the divine nation–that is, the Church–rule well, they rule in accordance with the divine commands, and never suffer themselves to be led astray by worldly policy. And it is not for the purpose of escaping public duties that Christians decline public offices, but that they may reserve themselves for a diviner and more necessary service in the Church of God–for the salvation of men. And this service is at once necessary and right. They take charge of all–of those that are within, that they may day by day lead better lives, and of those that are without, that they may come to abound in holy words and in deeds of piety; and that, while thus worshiping God truly, and training up as many as they can in the same way, they may be filled with the word of God and the law of God, and thus be united with the Supreme God through His Son the Word, Wisdom, Truth, and Righteousness, who unites to God all who are resolved to conform their lives in all things to the law of God.
Clement of Alexandria
Christians are not allowed to use violence to correct the delinquencies of sin.
Criticisms of Tertullian
Obviously Tertullian was perhaps the most anti-state mainstream Church Father there was. His teachings also included an anti-military stance, as seen in the following quote:
“Inquiry is made whether a believer is able to turn himself into military service… But how will a Christian wage war, indeed how will he serve even in peace without a sword, which the Lord has taken away? …The Lord in disarming Peter, unbelted every soldier.
It is for this reason among others that, in the influence of St. Augustine of Hippo and St. Thomas Aquinas who both supported the idea of 'just war theory' and the idea that certain acts of violence and control are necessary in order to secure the greater good, Tertullian has not been made a saint by the Church to this day (it should be noted also that Origen as well has not been made a saint by the Church, for similar theologically-based reasons).
All of these examples of that of spoken theology alone, but we must also recall that many early Christians expressed an unwillingness to participate in government mandate and command through their martyrdom. The following are just two examples of the words spoken by certain Church fathers before their martyrdom.
Polycarp
Eighty and six years I have served Him, and He has done me no wrong. How then can I blaspheme my King and Saviour? Bring forth what thou wilt.
These words were spoken before Polycarp was burned at the stake for refusing to offer incense of the Roman emperor at the time, being Caesar.
Ignatius of Antioch
I am writing to all the Churches and I enjoin all, that I am dying willingly for God's sake, if only you do not prevent it. I beg you, do not do me an untimely kindness. Allow me to be eaten by the beasts, which are my way of reaching to God. I am God's wheat, and I am to be ground by the teeth of wild beasts, so that I may become the pure bread of Christ.
Here again we see the Church fathers willing to die for God rather than live in order to please the mandates of man. So the nature of rejecting a government's authority (insofar as such means living rather for the Divine Authority) is not only present in several Church father's thoughts but also within the very deeds of the Church fathers.
Augustinian Minimalism
Besides the preceding examples of early Church fathers stating rather 'anti-state' philosophies, the more widely accepted and consistent St. Augustine has revealed a very politically minimalist view of the government's role himself, bordering even on a criticism of certain actions of rulers in such indirect ways as the following anecdote:
When [Alexander the Great] asked [a captured pirate] what he meant by infesting the sea, he boldly replied: ‘What you mean by warring on the whole world. I do my fighting on a ship, and they call me a pirate; you do yours on a large ship, and they call you Commander.’
Augustine's general dislike and distrust of the government stemmed from a theological understanding that is deeply held within Church teaching, namely that the striving for power is an essentially empty journey that leads only to sin.
God did not intend that man should have power over his fellow man.
Augustine's famous book 'The City of God' distinguishes between two cities, namely the City of God and the City of Man. For Augustine, the City of God belongs to those who orient themselves firstly to the Highest Good. The City of Man belongs to those who orient themselves to lesser goods. Augustine firmly believe that often times government power was lived for as the Highest Good because society largely considered it to be the common good. Unlike our system of living today, in which all things are in subjection to the individual's judgement, Augustine lived in a time when anti-religious, secular philosophers stressed the idea that man's workings in politics and rhetoric were for the common good, and thus for the Highest Good. It if for this reason that St. Augustine, as a truly impassioned and devout Christian man took such a great disliking of what we consider to be the 'government'.
It is this Augustinian minimalism that has still managed to thrive within Christian politics throughout the long years, and although our roots of 'obedience to government without trust to government' sentiments have perhaps 'dummed down' since we have experienced the blessing of having our morality sanctioned within law itself, it is easy to see where so many of our Church fathers were coming from in their general and sometimes specific dislike of government as a whole. It is a dislike that is likely to resurface in the Church in years to come.