I'm interesting in piecing together what religious practices amongst the urban citizenry would have been like in the century or so just preceding the dominance of Christianity - so let's say approximately 200 to 350ish or even 350 to to 400ish. That might be two different questions though. In order to couch the question I specifically mean amongst the urban populations in Italy or Greece (although they might be different?) and not in the frontiers or Near East. I ask because the way it always seems presented makes it sound like this dramatic replacement of the traditional Greco-Roman pantheon, but doing my own readings it seems to me that many of the core components were already in place (Neoplatonic concepts of monism to monotheism, consolidation of gods into a smaller pantheon, and Orientalization of Roman religion). So anything you know or recommendation for books or papers would be helpful. Cheers.
I have a generalized response in my answer concerning the move of Hellenistic religion towards monotheism. While all the parts of the Empire were on their own wavelengths due to slow communication and of course regional differences in worship, the idea of worshipping a single god during these periods was certainly organic than if it was a sudden lightning bolt that changed everything at once.
Religions typically had a head god already and due to a shift from city state politics towards a centralized imperial polity, the changes finally had become to ingrain in the Roman population. Mind you that by 200 AD, Greece had been in the Roman sphere for over 600 years.The Emperor already held the title of Pontificus Maximus, the spiritual leader of the entire Roman world, ruling under the authority of Jupiter. Despite Ares/Mars being an integral god in the early Roman civilization, it shifted as Rome Hellenized with its Greek influences to worship Zeus himself.
Over time, this admiration for Jupiter would eclipse other gods and some parts of the Empire just worshiped him and him alone, or Heracles.
Once they decided to become a Christian nation after Theodosius, The Emperor held the role of Pontificus Maximus in the West until the fall , but the East held it for effectively a millennia after until the collapse of Constantinople. And of course, the fact the Pope got it simply by power vacuum caused many of the theological and political issues for centuries more. The pope was effectively an emperor in all but name, but the Roman Emperor was both secular and religious leader who , left over from the ancient Roman times, could depose and appoint those as he saw fit. And thus, seen the papacy as inferior to his authority. And vice versus with the Pope, who likely resented the Emperor for how they abused Italy. Grudges last for centuries apparently.
The bottom links have the Brittanica post on Jupiter and my older comment that goes more in depth to help answer your question. I hope the Encyclopedia Britannica is reliable enough for this purpose.
https://www.britannica.com/topic/Jupiter-Roman-god
https://www.reddit.com/r/AskHistorians/comments/8ogxs0/comment/e03ricj
Edit June 8,2018 :Corrected from Hellisotic to Hellenistic.
Also Myrmidon79’s response is correct. The Romans conquered them by the mid 2nd century. But jdwright1989’s point about the cultural influence, which I referred to, stands as they were heavily influential to Rome’s development as were the Etruscan monarchy, due to Magna Graecia.
Interesting point. The Eastern Romans ruled over the areas formerly known for those colonies for centuries after the fall of the West until the Arab invasion of Sicily in the 9th century and the Normans completed in the 12th century.
Chiming in here on mobile as a late ancient historian to say that this very good question is honestly answered by an entire field of study. The names that fill the annals of Roman religious history spend much time just in these topics—Mary Beard, Simon Price, John Scheid, Fritz Graf, both Alfoldy’s, Andrew Wallace Hadrill, Clifford Ando (the list honestly goes on and on) have filled many volumes. So I just want to note that there is no simple answer to this query that doesn’t necessitate a great deal of material evidence, historiography and literary work, to say nothing of religious scholarship. Diving into books by some of the above or others would doubtlessly give you better footing than anything one of us could write on reddit.