Is it ethical to send my research proposal to a potential supervisor, when another professor has accepted to be my supervisor? I have contacted a professor and he accepted to be my PhD supervisor, but he want me to finish the application procedure by September. The institution that I am applying for is not in my home country, therefore I still have papers and tests to prepare (GRE, TOEFL) ... the process may take at least two months.

Is it ethical to send my research proposal to another professor (from the same university)? Knowing that I contacted him before and he only replied now asking me to send it to him.
Any person could change his mind about everything: universities, supervisors, jobs, etc... The important thing is to be clear, honest and understand the possible consequences.

I'm supposing that, at this moment, you didn't formally signed any document indicating the first professor as your supervisor. In this case, you could tell what is going on and indicate that will continue your conversations with both and make your final decision in the next days as they are very qualified and would be great supervisors. And reassure that you are doing your best to be ready for September, tests and all paperwork, as probably both have the same deadlines. 

Personally, I talked with three professors till I made my decision. I asked about possible projects and how I could fit in their research groups; read papers on their current work and talked with other PhD students about supervising styles, lab facilities, etc... to make an informed decision. 

If you already formally indicated one professor as your supervisor then check the rules.