I do not think Black Holes actually contain a singularity (a point of infinite density) at their center.
And so if they are made of particles then there is really only one option:
They must be made of so called Planck particles (which are the smallest and most energy dense particles theoretically).
Planck particles are thought to be extremely unstable but just consider that neutrons are also unstable but they are stable in a neutron star.
I think neutron stars are must be in some kind of fluid state (consider how two neutron stars would/could merge), so Black Holes also could be similar.