If it is surface dirt & grease you should be able to get it off with Simple Green (Diluted) or most times with warm water and Dawn Grease Cutting Formula. If it is stains that have been there awhile, then you may be screwed. Brake cleaner is scary, it is pretty hard on paint, whether it is Sprayed or Powdercoat and will allow staining down the road in the same area where you used it as the paint is compromised.
I had a Buell with staining on the engine (from a previous owner). I cleaned it to a point where it was grease free, but still brown stained. I then used HD engine color in a Rattle can and dusted it with Multiple coats, very dry until the stain was hidden, then after flash time untapped and re-taped to a break point where a paint edge could not be seen and sprayed on one regular spray can coat over that area. Road bike a couple years after that and it still looked like new when I sold it.
You might try 3M wax and grease remover, or similar, if you don't want to go the paint route. Pretty good product. Pricey.