I know people who would sleep with you before they make eye contact with you, so for all that find eye contact the most intimate and awkward act, you can bypass it without anyone noticing
Basically, look somewhere close to the person's eyes and you should be good
According to ScienceDaily :
Using eye tracking technology, researchers have demonstrated that people don't need to mindfully look at the eyes of their audience to be perceived as making eye contact during face-to-face conversation. Simply gazing somewhere around the face or head will suffice.
SOURCE: ScienceDaily