The goal is, as others have said, to reduce the friction between coins... or rather, to allow them to slide past each other smoothly: that coins don't do this is not completely because of friction.
But we want to do this by the intrinsic properties of the coins, not through adding a gas or liquid.
Normally, coins poured into a container will tend to align with the floor of that container. So in a swimming pool the coins will all lie flat, making them very strong in compression. If the coins can be randomly arranged instead, this would definitely help.
The shape of the coins is probably the major issue here, but also probably one of the things that OP is least able to change.
If you push two stacks of coins together, they will remain separate: they do not "smoosh together". It would help if the edges were rounded rather than square, so that if you pushed two stacks of coins together, they would smoothly interleave.
Similarly, if you press down on the top of a stack, it is extremely strong and stable: a stack of dozens of coins will not collapse in compression, even if the coins are imperfectly stacked. So it would help further if the flat surfaces of the coins were also slightly domed, akin to flattened M&Ms or Skittles. That way, imperfect stacks become compressible.
Consider the difference between pushing your hand into a box of M&Ms, and a box of stacked sugar cubes: the skittles let your hand slide in freely, the sugar cubes will resist you.
Lighter coins will have less friction, and also less mass to resist the swimmer/diver. They need to be as dense as water (so the swimmer floats), but not much more than that. Actually, to be more precise: the volume occupied by the coins and the air between them needs that average density. Aluminum is probably close to as good as you can get.
Teflon-coating coins wouldn't allow diving, since they would still basically be a solid in compression. They might allow one to swim through them.
Personally, I suspect even the above wouldn't be enough to make them swimmable. Simple solids are probably unlikely to accomplish divabilty, no matter how slick they are.
Coins that are made of (or laced with) magnetic monopoles would be one way: they would repel, and thus be slicker than teflon, as well as spaced out, the topmost ones even hovering a little.
This would allow for both compression and buoyancy, both important for absorbing the impact when you dive in! You'd also get splashes, waves and ripples.
If monopoles are too handwavey, another possibility, though I haven't checked it out, might be magnets embedded into coins such that the south face of each magnet faces out... and the coins being made of superconducting materials. Superconductors are repelled by magnets, but I'm unsure what he behavior of a superconducting object with an embedded magnet would be. Intuitively, it feels as if such coins should act kinda like monopoles, but nothing at all works as I would intuitively expect around superconductors, so I'm probably wrong.
Of course, even if this works, it means making coins out of room-temperature, 1-atm-pressure superconductors, which have not yet been discovered.
If the person swimming is very very light because of low gravity, then so can the coins be. This significantly reduces friction, and also compaction due to gravity: a swimming motion would churn the coins up farm more, and they would fall back in place far more slowly.
I'm not sure any one of these will be a solution, but some combination should be feasible, particularly if combined with other answers here (changing or forcing the separating material, vibrating, etc).