Typically sideline photographers have a 400mm or a 500mm long lens and a 70-200mm for close up on two bodies. For pregame they might switch to a ultra wide for coin flips.
That is right on the sidelines though. So you will probably want something with a 500mm (35mm equiv) at least.
I was stopped from bringing my Canon EF 70-200mm f/4 L IS into a Rockets game. The Canon EF 70-300mm f/4.5-5.6 DO IS USM is tiny with diffractive optics (DO) but doesn't deliver as good of images.
If the only limit is length, the Canon EF 100-400mm f/4.5-5.6L IS USM might be an option.