Is it covetous to want to get married? I'm not speaking of an example of a man and woman loving each other and wanting to marry, but rather a man or a woman who wants to find a mate? I go to a church that is mostly elderly people, so there is no Christian of the opposite sex in my life right now that I have in mind in particular, just a general desire to meet one.
Coveteousness is a form of greed where you desire what another person has. It is not the seeing someone's car and thinking you would like to save up an buy one like it one day. The coveteous wants that person's actual car and is willing to sin to get it.
There is nothing wrong with getting married, God recommends it. It becomes wrong if you are wanting to marry another person's spouse. "You shall not covet your neighbor's house; you shall not covet your neighbor's wife, nor his male servant, nor his female servant, nor his ox, nor his donkey, nor anything that is your neighbor's" (Exodus 20:17).