I am half way through a video on this myself. I quit using the syringes, gels, and other stuff. It was to frigging messy and complicated.
I usually just grab a bottle of water and cut the top off. With the slide locked back on the firearm. I dip the suppressor about 1/3 to 1/2 in the water and shake out excess on the way out. Then shoot for a bit and repeat this as necessary. I guess you could buy a fancy can or cup and all sorts of other stuff, but this method works well and costs about $0.20 to shoot all day, more often then not is doesn't cost me anything.
*Always read the instruction that are included with your suppressor or visit the manufacturers website before running your can wet.**
I use wire pulling gel also. It has natural rust inhibators in it, but it is water based so you do need to clean it out well and oil the suppressor afterwards.