I don't think you should just give up.
And, I completely understand the Cardinals position. Let's say, instead of the Cards, we are talking about the Greenbay Packers or the Cowboys. 100s of people would probably just setup websites and claim that they are in need of media creditals just to get better access as a fan. With 100s of websites requesting access, the NFL as a whole has to draw the line somewhere. Keeping it to only real Newspapers, Radio, and TV sounds reasonable.
They don't want their practices swampped with tons of reporters.
Now, on the "Don't give up yet" plan.
Do the Cards have enough media attention right now? No way. There was an entire thread about how the Giants and other teams have big writeups in the paper this week (and everyday), while the Cards had almost nothing.
I really think you should consider getting affiliated with one of the large media outlets in town. Send them all info. Say you'll work for free. You are now. Maybe you can get a deal where you write a few free articles a month or whatever and they can have an internet outlet for the Cards.
I could see them adding "For more Cards info logon to ASFN" giving the website address of course. ASFN would need a little extra police-ing due to all the one time flakes that may show up more often, but it won't be much more trouble than now.
Which media might you target? You could blitz them all and see who responds. Radio - 860 and 1060 might be interested. I see nothing wrong with having more than 1 reporter from one source. I'm sure other NFL teams have multiple reporters for 1 station. I don't know if the AZRep would give you the time of day, but they need the most improvement. Maybe the Trib would consider an affiliation to try to gain a leg up on the Rep.
I know nothing about TV, but you could try. You could be basicly a TV consoltant where you research developing stories and when one is worth of some TV coverage, you call up the real reporters and tell them what's up and they take over. That would give them cheap access to the Cards and they won't miss anything.
That's how I feel. Don't give up. Just go with the flow.