When men accuse you a lot of cheating, its either two things. He is the one cheating or you are giving him reasons to think that you are.
Unfortunately, it's not always that simple. Many times the past does contaminate the present & ruin the future especially if something extremely difficult to deal with has taken place that wasn't properly cleaned up. Then even without any valid reason to think the same thing is going on again, the person reacts as if it is.
Accusing someone of cheating for no good reason is often fear driven response. It is their way of saying "I'm afraid you would cheat on me because this has happened before" or "You matter so much to me but I don't feel I deserve you & when you figure that out, you'll cheat on me", for example.
But it could also be that he is or has cheated (on you or a previous one) so he's projecting that onto you. It's a way to keep you on the defensive. Is it possible he's cheating?
Dealing with the symptoms (his accusations) won't solve the real problem (what's causing him to be constantly accusatory). Until that happens, nothing you say or do can reassure him enough to make him stop & logic alone sure won't work, those accusations are emotionally based if there is nothing you are doing to cause them & he's not cheating himself.
Have you tried asking him what is going on now that is making him feel that you would cheat on him? Was he like this the whole time you've been together or is it new for him?
That sort of constant accusations can also be used by someone that is controlling & manipulative in order to keep the upper hand. It's a form of emotional abuse. Again, professional help would be needed to stop that effectively, you won't be able to change his attitude by yourself, it's too deep rooted especially the longer it goes on & it's on him to work on his own stuff.