I am currently reading two recently published books on Constantine that offer different viewpoints on the religious nature of this historic figure. In Constantine, Divine Emperor of the Christian Golden Age, Jonathan Bardill argues that Constantine was a solar monotheist and he was definitely syncretic in his beliefs, as the Christian god was easily interchangeable with Sol. He talks quite a bit about numismatics and there are great illustrations, but perhaps he is overly dependent on numismatics for his conclusions.
Timothy Barnes in his book Constantine: Dynasty, Religion and Power in the Later Roman Empire argues that not only was Constantine a sincere Christian, but he was at least a Christian from the start of his rule, if not earlier. As far as the numismatic evidence, he says "I regard the inferences often made from coin-legends and from inscription whose wording was not dictated by Constantine to the mind and religious beliefs of the Emperor as extemely insecure, since on close inspection such inferences usually turn out to be logically dependent on mistaken assumptions about the value of surviving literary evidence." (pg 17) Barnes points out that coins are very important to fully understanding this period, but they only play a secondary role to written sources. He specifically talks about the confusion that people exhibit over that fact that some Constantine coins have Sol on them. He quotes Andreas Alfoldi, who said that Constantine's "outbreaks of passion in angry letters rather than coin types represented his real emotions." (18)