We always include a slip of paper with the invitation that says something along the lines of, "If you'd like to bring a gift, G is collecting donations for XYZ at the party."
For his first birthday, it was a charity that created birthday packages for local foster kids. The second was Harvesters food bank. The third was an animal shelter. I think almost everyone* donates something (all three take used items or just things around the house so no one HAD to buy something new) and about half of the guests brought a present for him anyway.
People seem to like the idea of bringing something even if it is not for the birthday boy and of course they still get thank you notes. We open any presents for G after the party and take a photo of him opening each one to send to the giver so they don't miss his reaction.
Of course, as I write this I realize you just want to say no gifts and not create a plan to collect anything! SO...I've received many invitations that say "no gifts" "gifts not necessary" "just bring yourselves" "your presence is a present" and have never felt weird or pressured. I bring a gift for very close friends and nothing but a homemade card by my son for others.
*my MIL seems to be the only party goer that habitually refuses to do a donation. go figure.