I can take a guess at where you may have posted before. I haven't been on some forums in quite some time due to the politics of it all. While the comments there can be extremely rude, they do offer concrete information regarding laws in your area, so I'm hoping you can take what they say with a grain of salt.
I'm no expert, nothing like the experienced people of service dog forums, but what I feel should be emphasized is just how difficult it is to not only train a service dog, but a psych service dog, and for autism at that. Some tasks that are trained for austistic children are controversial. Also, it can be very difficult to teach psych service dog tasks, period. The safety of the dog is also always a big concern with autism, I don't just mean because of their tendency to grasp things too hard or be too rough, but I think you've probably gathered that.
Laws for public access rights for trainers and owner-trainers vary by state, and possibly even by city, i'm not sure. The Service Dog Central forum's homepage is a very good resource for different laws by location. (State Laws | Service Dog Central
Find out what your local laws are, and make sure you adhere to them, as well as making sure your name is not attached to a dog that isn't a candidate, or training that is not up to par. Again, it can be difficult to truly, properly train a service dog, and being that you would be training the dog for someone else, and not assisted by another trainer at a facility/through a program, it's going to be much more challenging, and this isn't the type of thing you want to just give a shot without a good amount of education and experience in the field of training, behavior modification and of task work.
Being a private trainer of a service dog also holds you somewhat liable, as I'm sure you know. If you truly feel it's within your expertise, I'm not going to tell you you can't, or that you'd be in the wrong for doing so, but I again just want to caution you about how serious not just training a service dog is, but an autism service dog. Training pet dogs and training a service dog for something like autism is a whole 'nother ball field. The dog has to not only be absolutely bomb-proof with an autistic disabled person, but has to learn to perform complicated tasks under what can be extremely
stressful situations for the dog.
Kudos to you for wanting to find the right information, and wanting to know the laws. I would highly suggest learning the ins and outs of the ADA, the FHAA, and the laws in your area regarding trainers and service dogs in-training, as well as finding a service dog trainer to mentor under.