Ultimately, the decision on appropriateness when writing CCC adventures is determined by the DDAL administration. Each Convention Created Content module must be submitted to them for approval before it can be played. Groups and individuals with a long track record of producing quality content are given more leeway.
It works out very simply...
- Tier 1 = Uncommon
- Tier 2 = Rare
- Tier 3 = Very Rare
- Tier 4 = Legendary, but not all that often.
A variety of common magic items are a fairly recent occurence. To my knowledge, they have not been explicitly included in anything except DDIA-XGE: Underworld Speculation, the introductory module for Xanathar's Guide to Everything where they first appeared.
How many? One
As for how many magic items: one, always one - regardless of length. Hour-long introduction modules have none, and Epics sometimes have more, but neither are part of the CCC program.
I can speak from personal experience with the CCC program. I am indirectly affiliated with a CCC writing group; they submitted a module for a convention I staff for. It had two magic item rewards, both very thematic. They were told to pick one or the other by the DDAL administration.
A Note on Precision of Language
The question says...
the process for submitting adventures from conventions to Adventurers League to become certified “legal” CCC-AL adventures.
...but it's not an accurate statement.
CCC adventures are sponsored by and affiliated with a convention they premiere at, but the creation process starts long before the convention takes place. They're not created freely by the conventions to "become certified" later. They are authorized by the DDAL administration to premier at a particular convention before writing even truly begins.