It's broken because Cleric will often carry Advantage better than the Luck feat.
As written, the item could be hacked by performing an attack or spell attack to remove any carried Disadvantage. If that's desired - then that's fine - it is doing what is intended - but if it is meant to be neutral as you write then it will need remedies (below.)
Disadvantage can be removed almost anytime.
As written, the Cleric can get rid of disadvantage almost anytime. The item doesn't specify what prevents the cleric from performing any type of attack which induces a roll (i.e. taking a sling at birds or fence posts) thus removing any Disadvantage. Additionally, if your cleric ever gets a cantrip with a spell attack (i.e. by multi-classing or taking a cantrip Feat), then there's nothing in the item description to prevent them from casting the cantrip over-and-over to remove Disadvantage.
This means that as written, 50% of the time between short rests, the cleric will be carrying Advantage.
Depending upon how many short rests the party take - that item could be as good or better than the Luck feat.
If that is not what you intend, and you truly want it just to give role-playing opportunities as you mention and not increase power, then there are some remedies.
One solution to make it balanced: make the rolls simultaneous.
If you truly want it to be random and non-hackable, one solution is this: a PC decides to flip the coin, throws it in the air, takes a swing or casts a spell, then the coin lands in their palm (or on the ground) and they discover if they were lucky.
Alternatively, the PC flips the coin but the coin doesn't reveal its face until after the action.