A much briefer statement on Christians participating in the military comes from the third-century bishop Hippolytus. As with Tertullian in my previous post, I must caution that no reasonable person would take Hippolytus' writings as authoritative at the level of Scripture, and there are plenty of instances within his writings (nude baptism, for one) that we clearly don't care to emulate today. That said, the Apostolic Tradition ascribed to Hippolytus provides us with another insight into the pre-Nicene perspective of the church. As with Tertullian, I have yet to find a contemporary source (any pre-Nicene source) who made any effort at all to refute the proscription on soldiers. This leads me to suspect that, whatever variations there may have been in practice, there was no serious contention that Hippolytus and Tertullian were wrong in their assertions.
Herewith, then, I excerpt from Hippolytus' Apostolic Tradition, a section of the regulations on who may be accepted for baptism:
A soldier in command must be told not to kill people; if he is ordered so to do, he shall not carry it out. Nor should he take the oath. If he will not agree, he should be rejected.
Anyone who has the power of the sword, or who is a civil magistrate wearing the purple, should desist, or he should be rejected.
If a catechumen or a believer wishes to become a soldier they should be rejected, for they have despised God.
(These quotes are taken from page 100 of the Google Books online edition of On the Apostolic Tradition of Hippolytus by Alistair Stewart-Sykes. Full source here)
There is another document, sometimes ascribed to Hippolytus, that is all the more blunt. Most historians I've come across in my search suggest that the so-called "Canons of Hippolytus" (also known as the Canons of the Church at Alexandria) are actually later than he, but still pre-Nicene. I cannot find the full text though the internet is loaded with identical quotes of the headings of the canons. They all agree that Canon 14 states that a Nazarene (that document's term for a Christian) "may not become a soldier except by order." I shall be indebted if anyone can come up with a full-text resource for these canons as I cannot find one. The closest I can come is a partial text in C. John Cadoux "The Early Christian Attitude to War" (full text here) in which he reproduces partial translations of the Canons along with two parallel documents (page 122 in the PDF edition). Rather than reproduce the variations in readings here, I refer you to the entire discussion (pages 119-128 in the PDF edition), which essentially says that soldiers were to be refused baptism unless they renounced their office, or at least refrained from shedding blood; and that no believer should voluntarily become a soldier.
Incidentally, the entire Cadoux text is worth further reading for those who would like to go into this subject in depth.