We propose a simple and compact slow-light element by use of an optical microcoil resonator (OMR) constituted by two microfiber coils. Based on the matrix exponential method, we solve the coupled-wave equations of the OMR with n turns of microfiber coils and obtain a general solution. Simulations indicate that a tunable slow-light propagation can be obtained by controlling the coupling coefficient between the two adjacent microfiber coils by means of regulating the voltage applied to the ferroelectric crystal. A slow-light time delay up to 62 ps with a bandwidth of 0.4 nm is performed at the wavelength around 1.5 μm.