How many ways can a processor be programmed?
Loads! At the end of the day, the processor works in a specific way, all languages convert into this operational form. If you want to work at the processing level, you could always try machine code or assembler but to be honest they are probably not the best option. Instead something like C (which has compilers for many many processors) is a good choice.
I doubt you need to write a new programming language - if the processor is completely new then maybe port some aspects of a compiler, but if the processor has been around for a bit chances are this has already been done for ya. - what are you trying to do, and for what processor?