iCloud storage and storage on iPad are completely different, so the simple answer is no, you can't buy more cloud storage to watch movies. iCloud storage is for backups. The only way you can have more room on your iPad is to delete material from your iPad. You take apps off you don't use. You can unsync music and pictures via iTunes sync on your computer. But you must delete, to make more room.
I had the same problem with all my kids TV Shows. And the above answer from rbrylawski is correct. But we also found another solution that works pretty good for us and can even watch our non-purchased movies as well. We purchased a small separate device called the Kingston Wi-Drive, which is basically a wireless portable hard drive. They come in 16, 32, and 64Gb. You can find them on eBay for a low price in some cases.
I would suggest keeping the entire series on your computer and syncing only a few episodes at a time over to conserve space.
You can also use an app like Air Video to stream video files from your computer to your iPad wirelessly, even when you are away from your home. The one limitation is that the app cannot stream any encrypted videos, such as those purchased from the iTunes Store.