I think your boyfriend should know why you are often quiet; and the two of you should work on ways to be together that don't require talking. Maybe, being a guy, he'll be glad that he doesn't have to chatter away all the time; guys talk somewhat less than girls, though I don't know if that's cultural or a brain thing. Probably a bit of both.
Just explain that sometimes it's tiring for you to talk, and you'd just like to be with him without talking much. You could do things together, like watching a movie or going on a walk, or doing something that you are both interested in (do you like video games? They require very little talking).
Don't worry about forcing yourself to talk. In my experience, the more you force yourself, the harder it gets. Communication is more important than speech anyway. Heck, if you wanted to, you could sit next to each other and send text messages. Quirky and weird, but in this digital age entirely common.
Just spend time together. After all, the closest couples can learn to understand each other without having to say a word. And just because you are autistic doesn't mean you can't learn body language. Many of us can, and do, learn body language easily, and can read it quite well when we aren't being forced to multi-task it with listening and speaking.