Rail Delivery Group would be those who implement any who new railcard. Although recent new railcard have been announced by the transport ministers and seem more of a political gesture now so I would also suggest contacting your MP. Any new national railcard would have to pass many hurdles and is very expensive to implement so I would suggest contacting as many people as possible to build up support including all the TOCs who make up the RDG, local and national press, politicians, rail user groups, if it's aimed at a particular demographic then anybody that represents that demographic for example an evening only railcard may be supported by the entertainment industry and pub/club trade bodies.
If it's a local railcard you suggest such as the Devon and Cornwall one then I'd obviously suggest targeting all the TOCs who serve the area in question to start with.
Any new railcard would likely have to prove it would make money for rail companies rather than take it away and cover all marketing and administration costs.
You will be able to get opinions and constructive feedback on whether people think your idea is likely to be adopted or a non starter and any modifications to consider if you post more details.