L'oreal Telescopic Liquid Liner in Carbon Black is the best liquid liner I have ever tried. It only comes in black though, which sucks if you don't want black.

What you can try, is NOT applying corner to corner. What I normally do is start in the middle of my eye and draw the line out to the outer corner of my eye. and then go back to the middle and draw from the middle to the inner corner of my eye.
Also, try doing smaller strokes as you draw the line on instead of one long one until you get better at it.
But yeah, IDK. Eyeshadow normally works better for the lower lid, but I seriously advise against using liquid eyeliner if you're going to use eyeliner on the bottom lid. 99% of the time it looks like you took a fine liner Sharpie and drew a crisp line on it. If you're going to do line the bottom lid with a liner, do it with pencil because it is softer.