Short answer: Kind of

You can if:

• you have an additional action to spare (uncovering then covering the coin would count as two object interactions).
• your DM thinks a closed fist "completely covers" the coin.

Long answer

The Rules as Written are silent on this exact point, but there are two main rules of relevance here.

Object interactions

The rules for object interactions on PHB 190 are the most obvious ones to apply here - ultimately you are interacting with the coin.

You can also interact with one object or feature of the environment for free, during either your move or your action.

Although this rule is not completely explicit about what "interacting with one object" means, several of the examples given on the same page suggest that this interaction is a one way-process. The clearest examples of this are:

• draw or sheathe a sword
• open or close a door

Furthermore the example of:

• extinguish a small flame

is pretty close to what you are talking about here, and is a one-way process.

So, as far as object interaction rules go, you could either cover or uncover the coin for free, but you would have to use your action to do both on one turn.

"Completely covering"

As the Darkness spell description says:

Completely covering the source of the object with an opaque object, such as a bowl or a helm, blocks the darkness.

So your DM will have to rule if simply enclosing a coin in your hand does the trick. The idea of darkness in D&D is so contrary to physics, that this is a tough one to rule, but your DM might rule that some of the darkness seeps through the gaps between your fingers, your hand is not sufficiently opaque etc.

So...

• If your DM decides enclosing the coin in your hand constitutes "completely covering" and

• If you have an extra action to use on both closing and opening your hand (eg from a class feature)

then you can go with your creative plan. Otherwise you might have to modify it a bit: use your only action but benefit the party, find a more 'darkproof' container etc.

You must take the Hide action to conceal your location

In combat, Hiding is never an automatic thing (unless some feature specifically says it allows you to). It always requires you to take the Hide Action.¹

Even if you cannot be seen, you can still be heard and hearing is enough for an opponent to discover your location.

The rules for Hiding state:

You can't hide from a creature that can see you, and if you make noise [...] you give away your position. (PHB 177)

Being in darkness in not enough to conceal your location. Concealing your location has a certain mechanic to it and that mechanic is called the Hide action.

Jeremy Crawford agrees here:

Q: My PC uses the invisibility spell, does he auto hide or do I still need to take the hide action to not be targeted?

A: The invisibility spell doesn't automatically hide you; you still make noise.

Invisibility here functions mechanically identically to your darkness for the purpose of the discussion of hiding in that it makes you unseen relative to the enemy. And neither will allow you to hide without taking the Hide action.

If you don't Hide, your location is known

So, if you are moving around an enemy and you don't take the Hide Action then you are heard and your location is known. In this case, they will be able to attack you (at disadvantage) in accordance with the rules on attacking unseen enemies.

When you attack a target that you can't see, you have disadvantage on the attack roll. This is true whether you're guessing the target's location or you're targeting a creature you can hear but not see. (PHB 192)

The enemy doesn't need to make a check (perception) and neither do you (stealth). Since you aren't trying to hide your whereabouts using the Hide action, they simply know where you are by hearing you.

Hide to conceal your location

However, if you take the Hide action you once again follow the rules for Hiding:

When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check's total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence. (PHB 177)

If you succeed and keep succeeding at that check, you are now "unseen and unheard" and your location is unknown. The enemy must guess your location in order to attack you. This falls under the rules for Unseen Attackers and Targets:

If the target isn't in the location you targeted, you automatically miss, but the DM typically just says that the attack missed, not whether you guessed the target's location correctly.

^{1 - An argument could be made that, outside of combat, taking the Hide action explicitly might not be necessary to be hidden, but this is outside the scope of this Q&A.}