It seems there may be one interesting encounter which is recorded regarding [Marcus Aurelius][1] and the [Christian population][2] at the time.  Marcus gives some credit to prayer by Christians within his forces to an event during his [campaign in the north][3] (here from *[Apology][4]*):

>  For having cast themselves on the ground, they prayed not only for
> me, but also for the whole army as it stood, that they might be
> delivered from the present thirst and famine. For during five days we
> had got no water, because there was none; for we were in the heart of
> Germany, and in the enemy's territory. And simultaneously with their
> casting themselves on the ground, and praying to God (a God of whom I
> am ignorant), water poured from heaven, upon us most refreshingly
> cool, but upon the enemies of Rome a withering(3) hail.

and this apparently caused a declaration before the Senate :

 

> Founding upon this, then, let us pardon such as are Christians, lest
> they pray for and obtain such a weapon against ourselves. And I
> counsel that no such person be accused on the ground of his being a
> Christian. But if any one be found laying to the charge of a Christian
> that he is a Christian, I desire that it be made manifest that he who
> is accused as a Christian, and acknowledges that he is one, is accused
> of nothing else than only this, that he is a Christian; but that he
> who arraigns him be burned alive. And I further desire, that he who is
> entrusted with the government of the province shall not compel the
> Christian, who confesses and certifies such a matter, to retract;
> neither shall he commit him. And I desire that these things be
> confirmed by a decree of the Senate. And I command this my edict to be
> published in the Forum of Trajan, in order that it may be read.
 
So, it appears that he experienced what he interpreted as a miraculous intervention, enough that he forbade punishment of Christians merely for their faith. Please note the author of the above document is not Marcus Aurelius himself, but the individual mentioned in the question, [Justin Martyr][5], so this writing is obviously 'biased' from a Christian viewpoint.


  [1]: https://en.wikipedia.org/wiki/Marcus_Aurelius
  [2]: https://en.wikipedia.org/wiki/Marcus_Aurelius#Attitude_towards_Christians
  [3]: https://en.wikipedia.org/wiki/Marcus_Aurelius#War_with_Germanic_tribes_166.E2.80.93180
  [4]: https://www.basilica.ca/documents/2016/10/St.%20Justin%20Martyr-The%20First%20Apology%20of%20Justin.pdf
  [5]: https://en.wikipedia.org/wiki/Justin_Martyr