Were I you, I would have a quiet word with institutional research or someone else who has all the numbers. One of the fastest way to shoot oneself in the foot during these discussions with administration is to insist that nearly everyone else is getting a better deal and not being factually correct or at least not being as right as one insists.
Unless you have seen a literal breakdown of who gets what, then you might be surprised that what you think is true (e.g., coordinators get two courses releases and summer pay, except in humanities) could be some other set of factors (e.g., Sally gets an extra course release for chairing the Gen Ed committee and summer pay for doing assessment on Gen Ed; George gets an extra course release for serving on the strategic planning committee and summer pay because that process is continuing through the summer) or sampling error (e.g., you know details for 10 coordinators and generalize to the whole pool). As the person on my campus who is responsible for the numbers, I sigh heavily when people make comments like "Most are better off than I am" and "I'm one of the only few who..." because that seldom is as true as one would like unless one has the full information.
For example on my campus, it is indeed true that the "average" salary reported publicly for tenured full professors is higher than more than 80% of those tenured full professors make by 10-20%. A handful of people who make a lot of money means that the mean (average found by adding up all the salaries and dividing by number of people) is very different from the mode (salary number shared by the most people) or median (starting counting at the top of a list ranked highest salary to lowest salary and stop at halfway down the list to report that salary). That doesn't mean the majority of tenured full professors are underpaid relative to their colleagues; that means a couple highly paid people either were in hot demand (e.g., keeping a director of an accredited program in which most people with PhD's have good non-academic opportunities, hiring a PhD to come here for a nationally hot field so we must pay nationally competitive wages instead of 50th percentile of CUPA (http://www.cupahr.org/surveys/fhe4.aspx
) for our comparison group in the region) or took on some very onerous duties that paying more money to someone already on payroll was the cheapest way to get done.
Another example on my campus was the chair who insisted she taught the most because she taught required classes that are always full and yet earned the least. Well, she looked carefully at people it was easy for her to find including her best friend and two allies with whom she spends a lot of time. However, all of those people were chairing accredited programs that require substantial extra administrative work as well as having strict limits on teaching loads by the accrediting body. The chair making the case never considered the chairs across campus whom she seldom sees who teach overloads (one person does double overloads) every term to full classes (compared to her one course release every term), have above our recommended number of advisees (compared to her zero advisees), and have lower salaries because they don't have terminal degrees and are still assistant professors with far fewer years in academia. In fact, the chair was average in terms of teaching load both for number of students taught and number of sections taught and her political capital on campus was lowered because the facts disagreed with her assertions.
A third example was the faculty member who carefully went through the preliminary course schedule and insisted that he was being held to an unreasonable standard of scheduling classes that many other people broke. He was right that a handful of other people had managed to get schedules that were strongly discouraged, but the solution was a change to those other people's schedules who had slipped through the cracks without official permission and a comment by the provost to the effect of: why have you brought attention to yourself again by highlighting how you don't want to do the job we have, but instead want to be at some other type of institution?
The OP didn't mention STEM problems, but I will mention that some people on campus who were indignant that STEM folks didn't teach a 4/4 (the protesters looked at the schedule and counted) were mollified upon having the math done for how one section of CHEM 101, for example, is actually six contact hours per week: 3 contact hours of lecture+3 clock hours of lab*2/3 contact hour/clock hour of lab+1 contact hour problem-solving. Consequently, two courses on the schedule for most STEM professors was actually more than 12 hours in a classroom/lab every week, even though it's only two preps, and there were no unaccounted for course releases.
To get back to the OP, you can try what Janewales suggests, but it likely won't get you any more money nor will it endear you to administrators since you've already been turned down for more pay. If you can be replaced at your current salary or cheaper by doing a TT search and someone will likely be grateful for the job, then you don't have the leverage you need to force a change. I have been in the room lately for too many discussions with the provost, president, and other high-ranking administrators that go along the lines of "We need someone who will do the whole job. Tenure only guarantees due process, not the ability of individuals to turn down tasks that are part of faculty jobs. People who don't want the jobs we have are encouraged to go elsewhere."
I'm not trying to scare you, but if you are at a smaller place and you are the primary logical choice for a task, then it's possible that you cannot get a response to Janewales' approach as "OK. Thank you for your service. We will go to another person on the list" (a possibility at a large place where many people could fill the role instead of the program being you and the one other person who already is carrying some other heavy service project). At a smaller campus, you might be able to negotiate an extra release while the baby is small if you can draw heavily on the "family" idea of a smaller campus if there's someone else who can pick up the slack and/or you can make the case that a cheap adjunct is worth the productivity to the college. Making the case for an adjunct to cover your course releases can be hard to do if adjuncts aren't very cheap compared to your salary; that's how many of those chairs mentioned upthread on my campus end up teaching overloads instead of getting course releases.
However, it's possible that a tight enough budget and a program that is already on the list as being underperforming in terms of numbers means cancellation of the program as a major to eliminate the need for a coordinator. Service courses can be coordinated through someone who isn't in the discipline, but can run a schedule and hire enough adjuncts. After all, if any one individual can be easily replaced, then that individual is easily replaced and it's a waste of resources to try to keep someone who is easily replaced by someone who is highly qualified and willing to work for the salary provided. I'm not saying I advocate for that mindset; I'm telling you the conversations that I have had and the administrative literature that comes across my desk as we look at some faculty in high supply fields who are making substantially more money than a brand-new assistant professor in that field and we regularly receive unsolicited materials hoping for even just an adjunct job.