You can't use someone's trademark without their permission. I don't know what you mean by "is there any way around this" because it's pretty simple. Can you elaborate on what you have in mind?
For example, let's say you accepted donations for a non-profit activity, and Pepsi donated some cases. If you used Pepsi's trademark on the materials for the activity to acknowledge their donation, it would technically be without their permission, but I doubt they would be upset.
Now on the other hand, if you asked Pepsi for donations and they declined, then you used their trademark on the materials under the heading "Cheap jerkoffs that wouldn't help us out", I think they might not be too happy.
So there might be some situations where you could use it but no one would mind.