What you want to ask for is 'Foamcore'. It's fine-celled foam sandwiched between two layers of thin cardboard. It's used to build architect's models.
Normally the foam is white and just the cardboard is colored, but there's a version that has black card with black foam--that's what you want.
Use a sharp, new blade to cut it and you shouldn't have any problems.
It's light and rigid and will keep its shape well. if you need to curve it, cutting a series of paralell shallow lines through it should let it curve to the shape you want...I haven't tried this myself though!