It is difficult for the first few times to put eyeliner. As long as you practice more, it will OK. When you put on the eyeliner, you shall keep calm and inner peace. Then, apply eyeliner on your eyelids gently. Besides, i recommend you to use soft eyeliner so that it don't causes damages to your eyelids as well as your eyes. Besides, soft eyeliner can help you achieve eye makeup easier.
Well, I am afraid that it may be iompossible. As you know, eyeliners are very easy to irritate your eyes and that is why u can' t stop blinking. But I have also heard that with time going on, this situation will just become better and better so u might as well just wait to get better. However, I am also told that our eyes keep blinking is cuz that our eyes are too sensitive so that you had better give up using it or you may choose some kind of anti-sensitive ones.