A plurality of deacons is called a diaconate. What is the reason for this vowel change ("e" to "i") for these words? Are there any other words that illustrate this?
The word deacon is an anglicization of the borrowed Latin word diacon (which itself was originally Greek), so the vowel change is the other way around. Over time, diacon became deacon.
The reason for the difference in the vowels between deacon and diaconate is likely because of when these two words were borrowed.
Deacon has been around in English for some time; the earliest uses in the OED date back to 1000 AD (early Middle English).
Diaconate was not borrowed at that time, nor was diaconate in any way derived from deacon when it entered English. Instead, it was borrowed directly from Latin; in particular, there is one OED reference in the 1700s and everything else is from the mid-1800s.
So, deacon has been around since the Middle English period and has been through a thousand years of vowel change, while diaconate entered the language fairly recently.
Another example of this: pope (from Old English) and papal / papacy (1400s): all came from Latin papa.