It sounds like there is an awful lot going on in your relationship. Let’s divide and conquer, shall we?
First, I would like to ask you to consider when you noticed sex had started "falling off." Were there other things going on in either of your lives that could have added stress to the situation? Perhaps those stressors have not been completely alleviated yet. Also, this would be something to consider contextually. How long have you two been together? Sex will ebb and flow within a couple’s relationship. I applaud that you have asserted suggestions to reignite the proverbial flame. What are you suggesting though, and have you asked him what he might find interesting, exciting, or new to try?
I don’t know where you left off in your sexual exploration, but I can recommend a variety of things to try. First up, lingerie and other fun attire. Have fun playing dress up … or even intensify the costume and head straight for the sexy school girl in need of a good spanking or the bad girl looking to "punish" her man Dominatrix-style. Just remember that while your goal might be to get his attention, this part also needs to speak to your sexual comfort and desire. Putting on a costume only to feel uncomfortable and awkward will only further exacerbate the negative rather than asserting the positive here.
Once in position, is sex between you two different, creative, or ho hum? Does it seem rehearsed? If so, I suggest finding a few new sex positions that work with your bodies and that you each find (or may find) enjoyable. When I say positions that work with your body, keep in mind that not everyone is a human pretzel. Unless you take yoga or are very athletic, it's best not to pursue anything too acrobatic or someone's likely to get hurt.
Another hot thing to try is a strip tease. You can dance for your partner, and even masturbate in front of him (he can’t touch you until you say it’s OK). There is nothing like being told you can’t have something to make you suddenly want it like it’s the last glass of water available in a desert.
Underneath all of this, I wonder how the rest of your relationship is going. You mentioned that the fighting has decreased, but has become more intense. Is your sex life suffering because something else is going on between you two that is not being addressed? How is the rest of your relationship outside of the bedroom? If there is a bigger issue underlying the lack of sexual activity, that bigger issue needs to be addressed. Even if you manage to have better sex, it will only fix things temporarily. And, if things are really bad between you, you might not be able to have better sex at all.
Above all, have an honest conversation with yourself. What is really going on, with you and with him? Then, when you know where you stand with everything, take the conversation to your man. Ask him the same things you have asked yourself regarding the relationship, the sex, and what else may be getting in the way. See what happens. Either way, good luck.