Once in a lifetime!
The following goes beyond what you asked as there are more factors than 'best lens' - it's also WHY this lens and what else that interacts matters. (Evrything interacs :-) ).
(1) Hire a D3s (world's best) or a D700 (superb but not as good) and lens. Or buy a used D700 :-). If you do get a D700 or even with your D7000, look at shots per second and buffer depth. Note that quality used may effect this. RAW, which is what purists will insist you use, will be slowest. Whether this influences choice is up to you. (Note that as D700 and D3s are full frame you can only use your X lenses in 6MP crop mode). Do NOT be put off by D700 12 mp resolution.
When comparing what you can expect to see with each camera at high ISO lean toward looking at real pictures and not just sensor comparisons. Decide how high and ISO you can go to get an acceptable shot compared to getting a noise free blur.
(2) CRUCIAL: *Whatever you take, practice in advance for the sort of shot you expect to be able to take.*
This can make a vast difference.
It's not just motion blue but which sorts of shots in a given sport look good or best afterwards.
I've taken numerous volleyball and table tennis shots. No hockey.
With TT and VB what you get can vary widely from what you expect until you have had some experience.
When somebody is setting up the ball to spike it in VB when do you take the shot? What looks best?
What difficulties are caused by ball speed or person speed and what looks most interesting.
In TT when do you shoot?
Where is the ball? How does this affect what you see?
Do you want the ball blurred or crisp. How much difference does this make.
What shutter speeds work.
Without flash, what shutter speeds MUST you have for any sort of quality?
What does that do to the types of shot you can take?
How much must you put up the ISO to get a minimum acceptable shot? What is the noise/blur tradeoff?
(3) Decide if the Tamron 18-270 will take the sort of photos you want. If so, take that.
The 50mm is superb for interest and low depth of field. At any distance you get no detail and focusing is generally harder.
A prime or short range zoom will restrict the range of shots you can do well. The 10 - 20 is very short range and he 50 and 90 too short for 'action way over there'. Again, practice will show you if this is true (it is :-) ) and how much you care.
If you don't mind cropping the results then a relatively narrow zoom range image then hiring something like the 70-200 etc may improve IQ enough to matter. I'd seriously suggest that you take your 18-270, go out and find some fastish action of the type you expect at the range you expect and ask yourself "what does this lens not do that I must have" and "what would I lose by using a "better" lense with less or far less zoom range. Then for outdoors take the Tamron :-). Indoors MAYBE something faster - but note that depth of field also falls and that's a small & fast moving ball that you want to be sharp.