I'll second (or third, or eighth, whatever we're up to now) the Tamron 70-200 f/2.8 option. I bought one used. I was a bit concerned, even though I've got a stellar Sigma 50mm f/1.4 and Tokina 100mm macro to boost my confidence in the third-party route. On the other hand, I figured the Tammy was the ONLY way I was going to get a 70-200 into my bag, and it was a really great deal, so I jumped. Glad I did; it is really a sweet lens! I haven't shot any sports with it, and yes, 200mm might be a little short, but it's such a versatile lens, and at least for me, I figured having to crop a good bit on 200mm fast glass was still better than trying to use my Sigma 15-500mm on sports in low light, where my ISO usually ended up so high controlling the noise was a huge factor.
Now, I can use the Sigma in the daytime and the 70-200 if the need arises to shoot sports under the lights. Not likely to get anything Sports Illustrated will come calling for, but then I'm not aiming for that, either.