I've made several and came up with some shortcuts. I do not "roll" the diapers as the instructions tell you to -- this is not only very time-consuming, but makes it hard to use the diapers afterwards since they are curled up so tight. For the bottom layer I start with a full roll of toilet paper. I wrap each diaper around it, overlapping to cover up the "open" side. I make a band out of 1/2 inch elastic to hold it together, which I cover with wide ribbon when I'm done. The elastic is a lot easier to work with than rubber bands, and it holds the rows of diapers together while I add on each layer. I stuff a baby bottle or bottle brush into the center of the toilet paper roll to anchor it and wrap diapers around it for the second layer. If you want to go higher than two levels, use a wooden dowel for the center and anchor it down with burp clothes, receiving blankets, or whatever. Then continue wrapping the diapers around it. The dowel can be extended above the top to tie on a topper such as a stuffed animal or doll or whatever. Once I found a special frame for an ultrasound picture, got a picture from the mom-to-be, and used that for the top.
I got an inexpensive clear plastic cake platter from the dollar store and used that as the base. I used a clear gift wrap bag to wrap the whole thing up with. I found that "wrapped" diapers rather than "rolled" made it easier to arrange all the add-ons like toys, rattles, small bottles of soap, lotio9n, booties, bibs. I always try to have a bib, blanket, or shirt embroidered with the baby's name front and center on the cake. You can really get carried away on these -- usually takes a Big box of diapers (newborn around 100) which is about $20 -- I get good quality diapers that can be used rather than waste money on the cheap ones. All the goodies can add up quick, and before you know it you've spent $75-80 easily. So start shopping right away at the dollar stores.
Have you also checked out the diaper wreathes that are being made now? Diapers that small come in colors now. It's a lot cheaper to make and gives the mom something to hang on the hospital room door and in the baby's room after. Good luck.