We introduce three soft-decision demodulation channel-optimized vector quantizers (COVQs) to transmit analog sources over space-time orthogonal block (STOB)-coded flat Rayleigh fading channels with binary phase-shift keying (BPSK) modulation. One main objective is to judiciously utilize the soft information of the STOB-coded channel in the design of the vector quantizers while keeping a low system complexity. To meet this objective, we introduce a simple space-time decoding structure that consists of a space-time soft detector, followed by a linear combiner and a scalar uniform quantizer with resolution q. The concatenation of the space-time encoder/modulator, fading channel, and space-time receiver can be described by a binary-input, 2q-output discrete memoryless channel (DMC). The scalar uniform quantizer is chosen so that the capacity of the equivalent DMC is maximized to fully exploit and capture the system's soft information by the DMC. We next determine the statistics of the DMC in closed form and use them to design three COVQ schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and/or receiver. The performance of each quantization scheme is evaluated for memoryless Gaussian and Gauss-Markov sources and various STOB codes, and the benefits of each scheme is illustrated as a function of the antenna-diversity and soft-decision resolution q. Comparisons to traditional coding schemes, which perform separate source and channel coding operations, are also provided