Launch, I haven't had a problem with getting my cover images to display correctly, but know from experience with other aspects of a business page on FB that they often have strict guidelines for image size, filetype, etc. It sounds like maybe your image is too small or not the right dimensions.
The Facebook Help
section has some info on this, specifically:
What if the image I want to use as my cover is too small?
Since your cover goes across the entire width of your timeline, the image you select for your cover has to be at least 720 pixels wide. This means you may not have the option to choose certain photos as your cover image, or you may get an error if you try uploading a photo that isn’t big enough. If the photo you want to use is too small, try uploading the photo in high resolution, or choosing a different photo.
There are also services you can try that will allow you to create an image using specialized software - you use your own images, or choose images from their stock selection, etc. Those might be worth trying? One that looks to be particularly well-developed: Timeline Cover Banner
Hope that helps!