My BD has one HDMI output and one Coax output. I'd like to connect the BD to the tv using the hdmi cable, and since my AVR doesn't have any hdmi connecters could I also connect the BD to the AVR using the coax cable so that both video and audio are in sync, or could it cause other problems? Thank you for any input you can offer me.
Your plan should work fine.
If there is a sync issue then your receiver may have an option to correct for this. Usually a sync problem is caused because of video processing that takes longer than the audio processing. It can also be a problem with your cable provider.
Plan B would be to use an HDMI audio extractor to provide a digital audio output.
Very helpful reply, Your idea of adding a converter is great and one with more slots could be a better midterm solution if I decide to add more source equipment.