I dont know how old your kids are, but I got my son a passport right after he was born. If your kids are in school, maybe a school id would work. I think if they are under a certain age, you do not need a photo id for them, but its nice to have a photo of them on hand in an emergency. A passport makes life a whole lot easier too. If you miss the ship for any reasons, it will be an expensive and tiresome ordeal to get back home without one!
On a side note, and this might work for a photo id: I attended a safety awareness program yesterday and picked up two great id kits. They were $20 each, but well worth it. You get two id cards (in one kit) one for the child and one for the parent. On it is a photo of your child, their dob, hgt, wgt, eye and hair color, and sex. On the back you can list 3 emergency contact numbers (home, work, cell) and by signing the card, you give your consent to treat the child in an emergency. You also get a disk with all the info on it, and you can purchase other items (cards, breakaway necklace, other kits, etc). In an emergency, its a no brainer to pull out the card and hand it to the police. The child can take the card to school, on trips, to grandmas, etc and should he need medical care, its covered. The best part is they will update the cards for free until the child is 18. For young kids, they recommend updating every 6 months, and for older kids every year. You can find them at kidzidz.com if anyone is interested.