I fill a small plastic syringe with solder paste.* The syringes I use are all plastic. The plunger tip is not rubber, but I am not sure that makes a difference. Generally, unless using a stencil, you will need to add a small amount of compatible liquid flux or other diluent. I use 99% isopropyl alcohol. I put a small amount of paste on a piece of aluminum foil, add the diluent (just a little) until it is more like ketchup, then use a small needle to apply tiny dots to the pads and proceed as usual. For very small SMD's, I use a reflow oven.
*It's quite hard to suck solder paste into the syringe. I fill the syringes from the back with the plunger removed (of course). With a fresh tub of paste, I fill several syringes, cap them tightly, and store in a freezer bag in a refrigerator (not freezer). You can also use whatever you have to put a small blob on the foil, if you don't have syringes.