If you are the domain owner you should be able to register with webmaster@domain or admin@domain. Afterwards you can set a free e-mail address, so you only need to use that e-mail for initial password retrieval purposes, in case you would rather not keep that e-mail address activated.
As the site cannot be confirmed to belong to a company rather than being a personal domain, are you able to register with your internet provider e-mail address instead? You can set a free preferred e-mail address after you have logged in for the first time.
Generally it is not a problem as most people have access to an internet provider e-mail address. Otherwise, we've allowed free e-mail addresses in the past and have seen a significant decrease in multi-related issues since that time, so it is the lesser of two evils.