What might a utilitarian say to try to justify the Omelas system?

A utilitarian would point to how much happiness the citizens of Omelas experience in order to justify its system of governance.

In assessing an action's value, the utilitarian uses the justification of how much good is expanded to as many people as possible. When philosopher Jeremy Bentham explains the concept of "utility," it is rooted the expansion of "happiness:"

Nature has placed mankind under the governance of two sovereign masters, pain and pleasure... By the principle of utility is meant that principle which approves or disapproves of every action whatsoever according to the tendency it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words to promote or to oppose that happiness.

Bentham suggests that the "measure of government" is to "promote the happiness of society."

This happiness principle can be used to justify the structure of Omelas.  The system of Omelas is one whereby all "happiness" is dependent on the child's "abominable misery."  The suffering experienced is far less than the happiness that is gained from it.  Society is able to experience pleasures such as knowledge, beauty, harvest, and skills because of the child's predicament. The result is that more people prosper and experience happiness in Omelas. This utilitarian would use this metric to justify the Omelas system.