I'd see if there was a compromise... a party, rather than a legally binding marriage?
Tricky one.
You both have to question what is really truly important. Lack of marriage or marriage... is love enough? Is there a middle ground?
What would you personally gain/lose in a marriage?
I'm married and my reasons for being so are probably VERY similar for the reasons my mates have for NOT getting married. Ultimately all of us are happy with our lives... for me, if DH hadn't wanted marriage I'd have 'yearned' for it but would have probably foudn some sort of compromise depending on his reason iyswim? (not knowing which one of you doesn't want it)
We have had a year of weddings this year, and everything else aside they were wonderful days of 'love' (yup sounds cheesy and probably is) and even our most devout cohabiters has conceded that actually they would like a celebration with friends, to acknowledge their relationship and love. They will never get married, but its hard not to be affected by one day of recognition amongst friends. I'm a romantic, I cannot wait until they celebrate their time together openly amongst us lot, even though their love is private.
A very tricky situation, but one that hopefully, as a couple, married or not, you can get to grips with in some way. Marriage doesn't make you stronger as a couple but it also means as much or as little as you want it to mean, and you can do it in many different ways, think outside the box.