It is very common for a couple to experience conflict and tension during niddah. Identifying the problem, as you have, is the first step to addressing it. When it comes to argument, the two of you can try to work together to notice when niddah is fueling or exacerbating an argument, and to help each other cool down. Sometimes just taking a time-out when an argument is beginning, or acknowledging verbally what you suspect might be happening, or taking a moment to express caring for each other non-physically, can make a difference.
Rather than avoiding each other or letting tensions build, it can help to discuss non-physical ways to express caring for each other during niddah in general. So can thinking of ways to spend time together, as you suggest.
Ideas are best arrived at by a couple brainstorming together. You can start by listing as many things as possible that you enjoy doing with each other or things you each have an interest in trying together. (It might help to think back to what you enjoyed when you were dating.) Then go through the list and see what might be appropriate during niddah, possibly with some modification. If there is a practical halachic question about a specific idea, please get back to us with details.