On my 39-year-old Sears tankless tabletop hobby compressor, I drilled a tiny hole (72 gauge?) in the brass fitting that reduced the 1/4" outlet to the airbrush fitting. It relieved the pulsing, and also lessened the laboring of the compressor, which did not even have an on-off switch! The TCP compressor is much smaller, has an on-off switch, a pressure regulator, and a moisture trap, and cost less ($80) in absolute dollars than my old Sears machine ($99 in US 1975 real dollars, or $432 in 2014 dollars).
However, there is an air leak somewhere in the plumbing--not on the outlet side, which I control--that makes it cycle on and off every ten minutes or so when I am not using it. Now, that's not especially bad, and doesn't put much of a load on the compressor, and reminds me it's still alive, so I guess I won't tear it down to fix that tiny but annoying leak. I've been in factories with absolutely huge compressors that cycled every once in a while (actually, every ten minutes or so), so I guess air can just leak out no matter how tight the seal.
I'm having a lot of fun with this little machine. And it is little!