In addition to the iOS apps, which I noted in this answer:
Will I miss out on anything by not playing Mass Effect 3's multiplayer?
You also get a 2-day Xbox Live Gold card in with the game. If you use this time strategically (ie, as you're nearing the end of the game) you might be able to spend a weekend playing the multiplayer mode to boost your readiness score. (Remember that it decays over time so you can't just use it whenever and expect to keep the bonuses.)
If you're anything like me, you've probably also got a few more of these codes kicking around. I'm not sure what the limit is on their use, but you might be able to buy yourself just enough time to get by.
Also note that if you haven't already taken advantage of it, each console has a limited number of "free month" Xbox Live Gold offers. If you create a new profile, and sign up for Silver, there's a chance you'll be offered a month of Gold for free.
Any of these methods would likely get you enough time to make an impact on your overall score, but remember that you can still get the best ending by just playing single player.