How do I install a custom ROM on a Prestigio PMT3677 I want to install a custom ROM like Cyanogenmod or similar on my 7" Prestigio tablet.

There doesn't seem to be any content on the net to explain what ROMS are compatible with this specific model and the steps to be followed to install a custom ROM on the device.

It's currently running Jellybean 4.2.2 but the tablet has extremely slow response times for most apps (and I have very few apps installed). Installing a custom ROM might make it a little faster and give it a nicer look.

I've already rooted the device using the same method as you would use to root the Prestigio PMP3670.

I don't want to just take a chance by installing just any ROM without following the right procedures for fear of bricking the tablet.
Custom roms must be ported separately for all device models. Installing a wrong ROM on a device even marginally different from the one it's intended for has the potential to brick the device permanently. If you cannot find a ROM made specifically for your device model, you are out of luck.