Thanks for the lengthy response.
...All we really learned about was freedom of speech.
Important stuff, but not useful in this case ...
With that being said, from what I recall a sports event is a public newsworthy event.
Yes. So you can take photos at the event... but if you use other people's photos you need permission.
At this point I am researching some smaller photographers, maybe even student or young professional photographers, that shoot the events that I am going to be covering. I will email them and see If I can get in written consent that I can use there photos in exchange to linking to their site.. Who knows maybe some will agree.
You will probably have a good success rate. Start with a just a couple of good photographers. Once there is some history on your site you will find it easier to get other photographers to sign up. They will be able to see that you are offering a quality product, and being associated with it is beneficial.
You need to understand that we photographers are always being hit up to provide our images for free - "... because the publicity is good for you." We tend to get tired of all of these outstretched hands. So it really helps when there is something of value being offered. Some very new photographers will be happy for any kind of linkage you can provide. But the experienced ones have probably already turned down sites like yours.
So... what can you offer them? Can you provide a shopping cart so that your viewers can buy the photos if they like them? You can take a 30% to 50% commission for handling the sale, the rest goes to the photographer.
Can you get them special access to the teams? Sometimes a news website can a Press Pass that a photographer can't get, and would like to have.
Are you going to have ads on your site? If so, then you can trade ad space for usage rights. The photographer can advertise that they take team photos, for instance. This is an easy sell to the photographer. If an ad would have cost them $100, but they get it for providing 4 photos that they would have only paid $15 each... well, you can see how they would think it's a good deal. And it's basically free for you to provide the space. The ads, if done well, also give you an air of legitimacy. It makes it look like people think your site is worthy enough to pay you money to promote themselves, eh?
Etc etc.... when you talk to photographers, ask them what they would like in exchange. See if there is something you can do that they need. You will have much more luck getting your photos that way.
Good Luck