One thing a friend mentioned to me early in the game was to focus on the animations. When I say "animations" I mean the actual game movements. It really does help. Once you get down what the correct point in the animation of the enemy is, it's a cinch to pull off counters.
Unarmed zombie that swings wide with one arm-- The animation has the zombie pull back then swing arm forward for a strike. Once the forward motion begins you can counter (regardless of the flash).
Unarmed zombie swinging two-hands down (hug)-- Once the arms begin to come down, counter.
Corpses with lanterns, shovels or firebrands-- Same concept as with the first unarmed zombie. The arm must be coming forward.
Corpses with stones (overhead attacks)-- You can counter once the zombie arches to their highest extent to bring the killng blow down, or just wait for the arms to come downward to you. Either seems to work.
Bloodshots-- Stay fairly close. Anything within 10-12 feet seems optimal. You want the bloodshot jumping in at you at about eye or shoulder level. Once close (based on the animation) just counter. It takes some practice but you should invest in this. It will up your scores significantly.
Those that are unarmed need a little extra attention. It's best to put a couple of rounds into their mid-section to soften them up before they go into the single armed wide swing. Soften them for the instant counter kill, or else, there is a chance they survive it, due to them being "tougher" enemies.
One important note that sometimes maybe people overlook..... You have to be facing the proposed counter, even a little. While in this game you can pan the camera behind you to look, it won't work if your back is completely turned to the enemy you are trying to counter. You have to be at least somewhat facing them, or their attack hits you.
Hope this helps. Just make sure you practice. It will come second nature if you practice a little solo.