First let me explain a little. I have created a male protagonist through which most of the story I'm writing is seen. He is a very serious character and rather quiet. Think of ToshirÅ Mifune in the film Yojimbo, or Clint Eastwood in The Dollars series by Sergio Leone. Another really serious character I can think of is Stephen Dedalus in Joyce's works but my character isn't quite so dark. He's just somewhat reserved and very dedicated to his view on life which is not a such a terrible one. He wants to see civil order in the world I've created. He meets a female character in his travels who he soon finds out he knew as a child. However, they only briefly came into contact as children. She could equally be seen as a protagonist in her own right, especially in the second part of the tale (book II) where they are briefly separated. The thing I've noticed is that the main protagonist seems a lot less strict to his principles and a lot more free when in her presence. He seems a lot more amiable to me anyways. At times his serious nature seems to bring about a comical relationship between the two as she is a lot softer and kinder. I think she brings out the best in him as he is defeated each time he is around her. He's no longer the stone cold killer. When they first meet she attempts to be kind to him like she is with almost everyone and he is a complete arse, and I think he sees this because of her. She in turn is very passive at first but in book II while traveling on her own for the first time becomes a little more hardy. There is a lot of balancing going on here and it seems good, after they first meet. The problem is that there is a great deal that takes place before the protagonist meets this girl and I feel that he is at times too serious. I feel like he doesn't need to be quite so serious. I feel as though serious might come to mean boring. The reader will never get to the good interactions. I feel like there is a workaround. Like Dune, I have a lot of characters and the protagonist is not in every scene but he is in the majority of scenes in the book.
I can definitely empathize with your situation. One of the protagonists in my novel is similar to yours as far as seriousness is concerned. The technique I used to not only make seriousness not seem boring but also interesting is show that character having unique interactions with others around him. Think about a situation when you met someone that was completely serious. There must have been hundreds of thoughts running through your mind as that person went from decision to decision. If you take it from the perspective of an outsider instead of the insider looking out, then there is plenty of ways for you to make a serious character interesting. Good luck with your story!
Please, take into account that "serious" characters like the Stranger with no Name and Snake Plissken do have a well developed dry sense of humour, they weren't conceived as "dull" characters at all.
serious does not equal uniteresting, and you have a good oportunity for character growth if he's unable to maintain his general demeanor when around the female MC. Keep him interesting, make him unique and people will read on far enough to watch his growth.
Try to develop your character in all aspects. In other words, make him multi-dimensional. By all means make him as serious as you want, but as mentioned above, perhaps he has a dry sense of humour. Especially important is that the plot challenges the character- I think you have alluded to this when you mention the love interest who brings out his kind side- but do not have the characters in some kind of balance. Make them clash over each other's different personalties, argue and fight. That will keep your reader interested, especially if it's one of those love-hate will-they-wont-they things.
This is also what popped into my head almost immediately. Overly serious characters thrown into situations that take a little more levity or tact on the part of the character force them to either bring down the whole room to his level or crack to the moment. The moment can be enjoyable without cracking his demeanor prematurely. The trouble would be if he is not just serious but super serious in light hearted moments. He would naturally bring down the characters around him which could mean boring scenes were the characters find themselves unable to act as they would normally.
I thought about it again and realized everything was perfect accept for the characters reactions to him, aside from the girl. The couple does not 'balance' each other. Its one of those 'at the end of the day' sort of things: "you were right I was an eejit back there" sort of thing. I mean they get in a pretty bad fight and are separated for a good portion of part II. It's a story that follows travelers like Dune and Lord of the Rings... Except its my own world, my own time period and my own creation. I don't have any silly elves or glowing blue eyed freaks. (I love those books so no worries) anyways I'm loving the characters now. I base them off of real interactions that I see on a daily basis or people I know. For instance, I saw a man outside a pub the other day who was yelling at another lad : 'You haven't a hint of Irish in you! All you are is a fookin Anglican arse and that's all yer ever going to be.' His voice was...something else. The poor "anglican" walked away with his head down...it was so sad. It was terrible but as I walked past them I was thinking to myself, that gives me an idea for my book! lol and I created two background characters based off of what I had seen.