Speaking as someone who has a ridiculous vagina that refuses to accept my OH without a major battle, regardless of how turned on I am, I have literally felt your girlfriend's pain.
One of the problems I found is that I started EXPECTING it to hurt, so whenever we tried it I'd tense up automatically because my downstairs always started wailing "No, don't make me, I don't like it!" Even though I did. Majorly irritating.
Apologies if this is far too graphic, but something we found works is oral with added fingery goodness. The oral gets very distracting, so it's easier to work one finger, then two, then three in. Plus, the fact that it's "just foreplay" takes a lot of the pressure off, because she needn't worry that you're going to unleash the Kraken on her any time soon.
It's important to be patient. If you manage to get your penis inside her even a tiny bit, and she says stop, then stop, but agree beforehand that you won't pull out unless she says so. Sometimes just a few seconds getting used to being stretched in that manner is enough, and you can work your way in slowly.
Use lube, and maybe consider a glass or two of wine before you try anything? I'm not saying get her wrecked, but I've always found that if I've had a drink I find sex a lot easier. I don't know if it's a placebo effect or something, it's just something I thought I'd mention.
Oh and if you're trying it missionary style... Don't. It makes everything tense up. Apparently it's easier if she's on all fours. Best position to have babies in, too, apparently, so if it's easier to get a baby out in that position, likelihodd is it'll be easier to get you in.