Could you be a bit clearer? Is it some sort of physical barrier (i.e. my lover in question lost the bottom half of her/his torso) or an emotional one (i.e. Phallophobia).
While I'm sure in an idealized world where true, platonic love exists then the subject of non sexual marriage may be a trivial one, in the real world it simply wouldn't last. Never mind all the biological urges you'd have to surmount, there's also the issue of selfishness. Among other factors, a good marriage requires open communication and cooperation. If you have needs that your partner is unable (or unwilling) to meet, it's kind of a slap in the face that they might also expect you to be just as happy with the arrangement as they are (and are unable to even field a guess at your side of the situation).
Short of chemical/surgical mind altering therapy to nip in the bud any desire or inclination you might have for sexual intimacy, the only other way I can think of to make the marriage work is ferocious "personal" intimacy or an open marriage. I mean, as long as you two still share your love and feelings for each other on an emotional level, it shouldn't matter how they proceed on a physical level given the restriction at hand, should it? I can't really imagine a marriage where a spouse is happy with their spouse's unhappiness working in the long run, something will give.