  The $SU(2,2)$-harmonic oscillator on the phase space ${\cal A}(2,2)=
{SU(2,2)}/{S(U(2)\times U(2))}$ is quantized using the coherent states. The
quantum Hamiltonian is the Toeplitz operator corresponding to the square of the
distance with respect to the $SU(2,2)$-invariant K\"ahler metric on the phase
space. Its spectrum, depending on the choice of representation of $SU(2,2)$, is
computed.
