Timeline of events that relate to dating coins with Christian symbols

Christian symbols did not occur on Roman Coins until the time of Constantine (307-337) and rarely until late in his reign. Then from 337 to 360 each emperor used Christian symbols at least occasionally. However, all of the coins of Julian II "The Apostate" (360-363) did not have Christian symbols. Then coins of his successor Jovian and the subsequent emperors frequently had Christian symbols.

312, Oct. 28.  The decisive "Battle of the Milvian Bridge" (just outside Rome) was fought between Constantine and Maxentius.
316  Ticinum minted the SOLI INVICTO COMITI type with a cross in the left field. (This begins Table 1.)
322  The first clearly Christian reference on AE coins was issed for Crispus. It has a chi-rho on his shield, c. 322-3.
326  Crispus, his eldest son, was executed by Constantine. 
326  The mint of Constantinople opened.  Constantine has the famous SPES PVBLIC type, c. 326.
330, May 11.  Constantinople was formally dedicated and the very common VRBS ROMA and CONSTANTINOPOLIS commemorative types began to be minted at all mints.
330  The very common GLORIA EXERCITVS "two soldier and two standards" type began to be minted.
335  Delmatius was promoted to Caesar (He has some GLORIA EXERCITVS coins with a chi-rho on the one standard.)
335  The GLORIA EXERCITVS type changes from two standards to one standard (and weighs less). Some have a chi-rho on the standard.
337  Constantine dies of natural causes (This ends Table 1 and begins Table 2.)
337  Delmatius (and others) are killed in a purge of relatives other than the sons of Constantine, leaving only Constantine II, Constans, and Constantius II as Augusti.
337  Theodora was honored with AE4 coinage. Some have crosses in the field. (The date of her coinage is not certain and may be earlier.) She was the daughter of Maximianus, second wife of Constantius I and grandmother of Delmatius, Hanniballianus, Gallus, Julian II, Licinius II, and Nepotian. Helena, mother of Constantine, has AE4 coins which are very similar to those of Theodora and it is therefore assumed they are from the same time period. (Helena's AE3 are earlier, c. 325-6.) 
340  Constantine II was killed during an attempt to invade Italy (territory of Constans), leaving only Constans and Constantius II as rulers. As a result, the city of Constantina (with mintmark PCONST) reverts backs to its former name of Arelate (= Arles).
348  A coin reform which introduced the very common FEL TEMP REPARATO types (in Table 4). There had been relatively few AE coins minted from 340-347 and they were only small coins. The new types were much larger and more impressive. Many have Christian symbols which became common on coins. 
350, Jan. 18.  Constans was overthrown by Magnentius, who proclaimed himself Augustus. (This begins Table 5.) Constans was killed shortly thereafter while fleeing. Magnentius issued an AE1 with a large chi-rho as the design, not just as a tiny symbol. 
350, March 1.  In opposition to Magnentius who was was in control of the West and Italy and marching eastward, Vetranio promoted himself to Augustus in the Balkans and declared it was in support of Constantius II, who was away in the East. Most of Vetranio's types (in Table 6) have Christian symbols, and one is very explicit with "HOC SIGNO VICTOR ERIS".  
350, December 25. Vetranio abdicated in favor of Constantius II upon his return and retired with honor.
351  Magnentius promotes his brother, Decentius, to Caesar
351, March.  Constantius promoted Constantius Gallus to Caesar to help in the East.
353  Poemenius revolted against Magnentius at Trier in favor of Constantius II. (He issued a type in the name of Constantius II which is very similar to the chi-rho type of Magnentius.) 
353, August 11.  Magnentius was defeated by Constantius II and committed suicide, as did his brother Decentius August 18, which left Constantius II the sole ruler.
354, winter.  Gallus executed by Constantius II for egregious misrule.
355, November 6.  Julian II pwas romoted by Constantius II to Caesar to help in the West.
360  Julian was proclaimed Augustus in the West and began marching east in opposition to Constantius II.
361  Constantius II died of natural causes, leaving Julian the sole ruler. Julian does not have Christian symbols on his coins.
363, June 26.  Julian II died in battle during his invasion of the Sasanian empire.
363,   Jovian became Augustus. Christian symbols returned to coins.
364, Feb. 16.  Jovian died (carbon monoxide poisoning from a charcoal brazier in his bed-chamber) and is succeeded by Valentinian I, after which Christian symbols are more the norm than the exception.

Other events:
260-268.  A coin with reverse legend AVG IN PACE is issued for Salonina, wife of Gallienus (sole ruler, 260-268). This legend, unique on Roman coins, has inspired speculation that she was somehow a closet Christian.
c. 330. The ruler of Aksum (also spelled Axum, modern Ethiopia in Africa), Ezana, converted to Christianity and began minting coins with Christian crosses as the central type.

Go to the main page "Christian Symbols on Roman Coins."