To specify a system fully, details of the timing constraints and load requirements of the relays would be required.
However, from my experience EnOcean devices should do what you require.
Depending on where you are located you will need to use the 868.3MHz, 315MHz or 902MHz variants to suit the regulators.
The standard TCM300x/TCM320x functionality in Mode 3 will allows 4 switches to be tied to 4 outputs. So 3 off devices would drive 12 channels. However with some simple additional circuitry and some changes to the firmware you could readily drive 12 channels from a single device.
The standard PTM210x can implement 4 off push buttons, so you would only need 3 of these devices for 12 channels. They are self contained, not requiring any batteries, as they Energy Harvest enough energy from the action of pressing the buttons to send the required messages.
Range is typically 30m in buildings or 100m in open spaces.
Total cost for 3 off TCM300x/TCm320x devices and 3 off PTM210x devices should be under £150 or under $200.....
You would just need to add circuitry to drive your relays noting that the maximum current from each output is 2mA at 3.3V so depending on your relays, you may need a transistor between each output and each relay...
Do let me know if you require any further assistance.
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