Dynamic nonlinear magneto-optical-rotation signals with frequency- and amplitude-modulated laser light have been observed and investigated with a spherical glass cell of 3 mm diameter containing Cs metal with inner walls coated with paraffin. Intrinsic Zeeman relaxation rates of γy/ (2π)≈20 Hz and lower have been observed. Favorable prospects of using millimeter-scale coated cells in portable magnetometers and secondary frequency references are discussed.