It’s a hard sell if you don’t have an in at the agency. There are 1.5+ million nonprofits in the US. If you gave free services to all of them you’d never have time for the paid work. So you either need a friend on the inside to pitch the idea for you (look through your donor list), or have a compelling reason as to why it would be a major boon to your nonprofit right now to get the work done. If you can offer them some props at an upcoming event, or a byline on your website it might help (but not much).
You might have better luck in trying to get a discounted rate on some services, and have other services donated. Also be willing to pay for any recurring monthly expenses would help.