All those other Coins...

[Yuillegan]

If you're not going to draw upon enhanced durability when you're batted around and set on fire, what are you holding it for?

Agreed. It isn't like Christos hasn't had opportunity. And surely other wizards would recognise signs of demonic influence. The brimstone smell alone...let alone subtler things.

I just can't see it being any of the Senior Council to be honest. I did hypothesise based on the OP question though. Maybe Ancient Mai just for the reveal factor...but why would she bother? Also it wouldn't add up with any of them having a Coin considering earlier things in the series. The Gatekeeper seems to trust them all and points out that while the Council is harsh it can be necessary at times.

[BrainFireBob]

Impressing people at parties. Cristos is totally that guy.

[KurtinStGeorge]

Jim said they each have a powerup; that's different.

We know LtW's shapeshifting isn't just skill related
Rashid has his eye
Ebenezer has the Blackstaff
One, IIRC, is a saint/has access to faith magic. Martha Liberty is very tight with the loa; between that and her name, Santeria priestess is quite possible.

That leaves Christos, Merlin, and Ancient Mai.

Ancient Mai can identify a Foo Dog on sight; I would be surprised if she could conceal such. Plus she's ancient- she's aged, and the coins work against that.

Merlin and Christos are your two real possibilities.

I believe Jim has said that Ancient Mai is some kind of expert with magical constructs.  Also, if she had a coin; which I seriously doubt, I would bet it could keep her internally young and give her the ability to project an older version of herself to maintain her image and change to a much younger appearance whenever she wished.  The later wouldn't happen very often.