Words are important!! An "Enfield" is commonly taken to refer to the P14 (Pattern 1914) and the Model of 1917 made by Winchester, Remington and Eddystone during World War I. Most all started as blued, some changed to parkerized - Winchester always nicely polished - Remington and Eddystone tended to be less polished, but not bead blasted. USA did major overhaul program in WWII where metal often re-finished into a form of parkerizing, after blasting the metal.
If you are referring to a "Lee Enfield", totally different rifles. There is a No. 1, a No.4 and a No. 5 most commonly still being used / bought / sold. As above, generally, black Suncorite was correct for WWII and later production and re-furbs. Earlier WWI typically built with blued parts.
So need to correctly identify which rifle you are asking about, and which era that you are trying to reproduce. Depending on time, can be perfectly correct to have a blued No. 4, with appropriate dates, or it could be coated in Suncorite, again with those appropriate date.
I would agree with above that a "flat black" coating probably "most generally correct" - these were military arms - not meant to be sparkly and shiny.