Ceramic resonator instead of LC tank in a quadrature demodulator
It depends whether you are going to use varactor tuning to keep the quad circuit exactly on song. If you are, then it's unlikely that you'll get much benefit from a resonator (probably much more of a hindrance). You might also consider that the transmit signal you are trying to demodulate may not be locked precisely to a tight single frequency and, of course, it may drift with time and temperature. Been there, bought the T-shirt and in the end I phase-locked my small transmitter because it was subject to a really extreme range of temperatures.
It made designing the receiver easier but, it still used varactor centre-frequency tuning. Reasoning: varactor control is very effective and it's quite easy to use the demodulated data (integrated) to push the varactor control in the right direction. It does require that the data transmitted is DC balanced i.e. it has zero net DC energy content (such as when using a scrambler or Manchester encoding). So the benefit is that V-tuning is actually solving receiver drift problems that a resonator cannot fully do.
It also depends on the bandwidth of your signal that you hope to demodulate. Too much bandwidth may just result in poor results when using a resonator.
There are probably other pros and cons.