I agree that the website is really important, but I also know that a lot of times that can be a tough process to get more/more current information on the Spirit Squad page since that's typically not an administrative priority. So, if your coach can't get that changed I would really hit the social media like everyone else has suggested!
One thing that I don't think has been mentioned is YouTube - I like when programs have a coordinated "team channel" with clearly labeled videos (rather than everyone just posting videos in a disorganized way). While this seems a little dated with all the other social media options, if people Google your team, often the YouTube links will come up near the top of the results and allow them to see more current info/footage from your team to give them a better sense of the program than your current athletics website. Plus you can still link the videos to Facebook/Twitter. I'm sure there's a more scientific way to steer the Google results, but that's worked for me in the past at the old school I coached at where we were in a similar situation to what you've described.
With Facebook/Twitter, I think the regular posting is key, but I also stress to my team that they need to share/comment on what I post so that we get a wider reach. Me just posting doesn't do too much, but when they all share what I post, I see our reach increase exponentially, so I think that's an important part of the social media aspect.
I also directly mail/email information to HS and AS coaches on a regular basis. This is a little more time consuming - so I guess it just depends how much time you want/have to invest. I have a pretty solid database of email and mail addresses for AS gyms in the northeast and Midwest, and a smaller one for HS coaches/programs. I'm happy to share if it would be helpful to your team, just message me!