Thanks for your question. There are two substrates to consider when identifying the best solution: the rubber mat and the trailer wall.
For the rubber mat, neoprene or nitrile adhesives often work well with a variety of rubbers. The two I would suggest for testing are 3M™ Neoprene Contact Adhesive 5 and 3M™ Nitrile High Performance Plastic Adhesive 1099-L. Both are solvent based adhesives with low viscosity for pumping and spray applications. I would try Contact Adhesive 5 first unless the rubber is highly plasticized in which case you could start with 1099.
The other consideration is the wall material. Whether it is a flat panel (metal, paint, wood, etc) or frame posts (bare steel, aluminum, powder coated). If you have any additional details you’d like to share, that might be helpful to get closer to a specific solution. Please let me know if you have any follow-up questions.