Since your boyfriend entered without inspection (called EWI), then he has one option to become legal in the country. Unless the law changes (as it did under the LIFE Act in the year 2000), your boyfriend will need to apply for an immigrant visa at a U.S. consulate in his home country -- and will have to submit an application for a waiver to overcome his illegal entry into the U.S. Waiver applications are very complicated because they can involve psychological evaluation of your relationship with your boyfriend. Again, to apply for the waiver and immigrant visa, your boyfriend will have to leave the U.S. The U.S. consulate may take several months to decide his case.
Please contact a reputable law firm for assistance (Note: that most out-of-state attorneys can legally help you because we are permitted to practice federal immigration law outside of our state of jurisdiction).