Hmm sounds like a tricky situation! Did you live with your boyfriend in the US? If you lived with him for 2 or more years, and can prove it, then he may be eligible for an unmarried partner visa.
Aside from that, does he have any British/EU ancestry in his immediate family (e.g. parents, grandparents)? If one of his immediate family members was born in the UK or Europe, he would then be eligible to live and work in the UK on an ancestry visa.
Beyond that, the only other option would be for him to work in a shortage area -- is his current occupation in an area that is considered to have a shortage of employees in the UK? (e.g. teaching, nursing, etc.)
Failing all of those options, is marriage an option for the two of you? Unfortunately, getting a visa to work in the UK is very difficult if you don't fall into any of the categories I mentioned above.