If it won't take grease than the pin more than likely is either rusted or packed with dirt and or hardened grease.The right thing to do is remove the pin and see what the problem is.That being said,you can remove the zirk(grease fitting)and try to spray penatrating oil in the hole and all over the pivot point.Like Semi Retired said you can even put heat.Center the heat at the end of the pin,once you get it nice and warm, again with the oil(I like PB Blast).Rock it up and down,spray some more.Put zirk back, grease.If that doesn't work, pull the pin.
If you're using a manual grease gun, try putting some auto trans fluid in the gun, hold it upside down and pump it in. If it is hardened grease it will sometimes push through. If it has had king pins replaced recently they may have put the seals in upside down.
Okay.....Im gonna ask this question.....cuz I dint know what a "king pin" is ......other than the thing on the trailer .....which you all are clearly not referring to here.....
Buy a harbor freight air grease gun. I have one and been using it for years. It’s very very very powerful. If that can’t push the grease through, then you have a problem that requires dissemble