CreateSpace (Amazon's paperback self-publishing imprint) does not advertise that you can make hardcovers. They offer paperback, audiobooks, and a couple other options, but I wanted to make a hardcover version of Sal, Captain of the Baby Guards. I sent them an email, and they told me they do offer that service. You just have to contact them about it.
It costs $99 to set it up a hardcover, and then you have to pay for your own books (base rate + per page rate) and distribute them yourself - through a website or in person, for example. You can choose laminate case (glossy hardcover with the picture right on it) or library cloth with a dust cover (it's a little more expensive per book for the latter because you pay for a dust cover in addition to each books' base rate and per page rate). You also have the option of BW or color interior but like paperbacks, color pages are more expensive.
The representative was very friendly, but every time I asked a question, he would usually take 1 - 2 days to respond to it. (I could never get ahold of him on the phone and never did he return my calls, so e-mail was our sole communication.) That was a little frustrating. When we finally worked it all out, I told him I wanted the library cloth. He made it so a separate file was created on my account with a special icon. So, now I have two "Sal Captain of the Baby Guards" titles with slightly different icons.
Once it was set up, I went onto my account and paid the set up fee. (I didn't even realize I had a "cart" button until I did this.) Supposedly, it takes 10 days from payment to set it up. However, I thought that was the end. Nope, the next business day, there was action required on the hardcover. I was able to give it an ISBN (free through CreateSpace or you can enter one you purchased; purchased ISBNs are portable they transfer between publishing houses if you want to switch. Free ones stay at the publishing house that assigned them. But if you are changing publishing houses, you are probably going to want to upgrade or change the book to a new edition anyway.)
Once the ISBN was assigned, I could upload the information I wanted on the inside front and back flaps (because I chose a dust jacket). You can use a text file, like ".doc" or you can upload an image if you want your picture or some other graphic. The image needs to be of both flaps front and back. It also should contain words and exactly how you want the flap to look. Since I didn't have anyone design this for me, I went with straight text. I do not know if I will be able to adjust this in the future without another set up fee. Once you submit that, you get an message saying they will let you know when further action is required by you (or the "we're working on it" message). When you migrate away from that it will say you didn't save, but there is no save button - just ignore it. I did, then I went back in to check and everything was still good. You can click a link that takes you back to the "we're working on it" message.
I don't know yet if they will use library binding or glue or what other options I will get. I am not that far in this process that began weeks ago. I will keep you posted, though. I do hope that my going through it will make it easier for any of you if you want to publish a hardcover of your book.
I think a hardcover will be a good investment - especially for a children's book. Although I have to order and sell all hardcover copies myself because they tell you it will not be listed on Amazon, I have my own website, so this is not a problem. In addition, I can use them for trade shows if I decide to go that route in the future. The only difficulty was deciding on laminate or dust jacket.