To dye using commercial spirit dyes such as Fiebings:
1) Eliminate the daubers - they are fine for edges and touch ups but that's it as you have found out.
2) Re-dampent the leather with warm water - not sopping wet just damp. The dampness helps open the pores to the dye and evens it out as well.
3) Apply the dye heavily - a cloth works good as noted (although I've never worried too much about lint free and have been doing leather work as a pro for 40+ years), a sponge, or use those cheap foam paint brushes.
On the other hand I generally just dip the whole item in the dye bath - I use those cheap plastic storage boxes from Wally World. It takes at least a quart of dye to do this, but not so much to completely submerse the piece - just enough so you can swish it around and get all parts covered. Then hang it over the open container and let it drip off the extra, Before it's completely dry, wipe it off with a clean dry rag.
3) Once it's completely dry take another clean cloth and buff the whole thing real well to remove the dye residue left on the surface.
4) To soften use any good leather conditioner such as Lexol, Neatsfoot oil, or Extra Virgin Olive oil. My favorite commercial conditioner is Montana Pitchblend which smells great. I mostly use my own home made dubbin - a period mix of tallow, beeswax, and oil. And with all due respect to the comment above one should apply the oil LIGHTLY to both the inside and outside. Let the oil dry thoroughly and then apply a second or third coat ONLY if need be. Over oiling leather weakens and eventually damages it beyond repair but breaking down the cell walls.
Once you've got a coat or two of conditioner on and dried, just work it back and forth with your hands or over your knee. Should take just a few minutes to get it right.
I do prefer natural stains over man-made chemical stains. iron oxide, (rusty nails soaked in vinagar) makes a great looking stain, and is PC!
While I too prefer period dyes whenever possible, vinegar black is in fact a type of chemical stain - it's chemcical name is ferric acetate and works via a chemical reaction between the residual tannins in the veg/bark tan leather and the iron in solution. In fact if one wants the best dark black wet the piece down first with a good strong infusion of black tea or oak bark or walnut dye - these all add extra tannins to the leather - and then apply the vinegar black.
Another good period dye is log wood, which can be purchased from several sources.
Commercial dyes on the other hand are powdered pigments in a spirit solution.
for an more even stain on leather use a water stain, an oil stain will be somewhat mottled
A bit confused here - this sounds like your talking about wood stains maybe. While there are the water based leather dyes available (so-called Eco dyes and the low VOC institutional dyes used in schools where fumes of the regular spirit dyes would not be good), most commercial dyes such as Fiebings are spirit (alcohol, toluene, etc) based and not water or oil based.
In fact the so-called oil dyes as made by Fiebings are the top of the line leather dyes - I say so-called because there is in fact no oil in the product.
Old timers such as myself have and still do make "oil" leather dyes at times, but it's just a matter of adding a bit of light saddle oil or EVOO to the spirit dyes.
BTW - for some very good info on Period" leather and leather care see here fro several articles:
http://www.jarnaginco.com/Leather & equipment articles.htm
