Have them register for anything they DO need at a local Target or Walmart or Babys R Us. After all, even the bouncy chair wears thin after a couple of babies!
Then contact ALL the relatives for a shower- even the ones that can't come. Since the couple would not ask for any kind of help for themselves, you, the person doing the shower, can do it FOR them. Just let people know when you're having the shower and that while the couple has a lot of the things they will need, GIFT CARDS WOULD BE APPRECIATED, YOU'RE SURE!
This is totally polite and acceptable now. After all, everyone needs diapers, etc. when they have a new baby and anyone who HAS had a baby knows that! it might not be as glamorous as some gifts, but the real point is to celebrate a new life coming into your family and to help out the new mama as much as you can.
For the people who cannot come, you could arrange a 'virtual' shower using computers and a webcam. Or ask people to record messages for the new family and to post them on YouTube, which is free and easy to do. A nice thing to point out to people is that if they record a little message and either email it or put it on YouTube, the new daddy can see it overseas no matter where he is stationed. That way he gets to feel like part of the shower is for him too.
Or just say " We really wish you could be here, but if you can't please send the mama a card with YOUR best baby advice and support" Most people will send a gift card as well.
Babies are a happy event- but they take a lot of work and money. Your family and friends know this and they most likely know that the new mama won't want to feel like she is a burden on anyone- so they will want to help out without making her feel that way as well!
You're a nice cousin to put so much thought into this! Good luck and congratulations!