Any suggestions on how to convince your publisher that your story is good, and that it would be a good idea to publish it?
If the publisher does not want to publish your story, then at least one of these is true:
I'd focus on #1. To convince the publisher, you'd have to say something that isn't in the text. If there's something relevant to say that isn't in the text, that is a sign that the text does not yet sufficiently convey the goodness.
My advice for #1: Improve the story.
As for #2, proceeding under the assumption that the publisher doesn't recognize the goodness of your story is fraught with peril. If the assumption is true, that means they don't know what they're doing. If they do know what they're doing, then your attempt to persuade will be at best a waste of time, and at worst insulting.
My advice for #2: Whenever you catch yourself imagining that a publisher just can't see the goodness in your story, try to find another interpretation. If you can't find another interpretation, reconsider whether you really want to publish with a publisher who doesn't know what they are doing. And make note of how often you insist on this interpretation.
As for #3 and #4, those are all signs that this is not the right publisher for this story at this time. If a story comes close to meeting a publisher's needs, they'll usually tell you that, and clearly. Otherwise the story probably is not within range of persuasion.
My advice for #3 and #4: Seek publishers whose current skills, preferences, and business model match your story more closely.
There are many ways to impress a publisher.
The most obvious and effective way is to show them that you're a professional. Make sure your manuscript and cover letter has been proofread and edited. Make sure there aren't any typos or glaring editing problems, those are sure signs that you're not a professional. Make sure you have a neutral third party go over your manuscript and give opinions and look for errors. Your close family and friend don't count, they're going to tell you the love it and that's not what you need. Never /ever/ send them a first draft. You should go through at least a half dozen drafts before you even consider sending it to a publisher.
The next step is to make sure you do your homework about the publisher. Make sure they accept the genre of manuscript you have. Don't send a mystery publisher your romance novel. Also make sure that they are accepting manuscripts. Some publishes only accept new submissions at certain times of the year.
If the publisher does reject your manuscript, move on. Don't try and argue with them, you're not going to win and you'll be making sure that they never want to publish anything of yours. And publisher do speak to each other. Especially in the smaller houses, at lot of staff work for multiple publishers. So if you make an ass out of yourself to Publisher A, and they happen to work for Publisher B and C as well, you can bet they've passed along the memo to them not to consider you. A lot of editors and publishers have blogs and Facebooks, and you can bet there will probably be a post saying "Guess what this jackass just said to me..."
In general, acquisitions editors know what they're doing. If they reject your manuscript, it most likely means they don't think it will sell very well with them. Most of the time (unless you make a jackass out of yourself like I mentioned earlier) rejections aren't personal. Publishers are in it to make as much money as they can and if they don't feel they can make money off of your manuscript, they won't try.
And don't let that discourage you. 99% of writers have tons of rejections under their belt before they finally get an acceptance.
For nonfiction, write a good proposal.
I searched the web for an explanation of what publishers would expect in a proposal and created mine from what I found. Basically I used a one page explanation of my idea and why I was the best person to write it. To that, I added a ten page chapter-by-chapter description of the entire manuscript, and then three sample chapters. This was my proposal.
I started sending it out with a one page cover letter where I tried to offer a short reason why I was sending to the particular editor/agent. Use a spreadsheet to track who you send it to and when you sent it. If you don't hear back in 6-12 weeks, assume the worst. Always try to keep it out to at least two or three at a time. If someone rejects your work (or the time to live on the proposal expires), have a few places in mind where you can send it next. Look for similar works from small publishers and query them.
This is what worked for me. A small publisher who had published a similar title picked up my book on the basis of the proposal. I'm almost finished writing the first draft. It's tentatively titled Dopefiend (apologies to Mr. Goines) and forthcoming from CRP in Sept 2011.
Start a blog and post an excerpt from your story in serial form on the blog. Do some minor promotion but don't go overboard. Gather thousands of readers for your blog who post comments like, "I'm really into this story. Hurry up and post the next installment!"
Then go to the publisher and show them a Google Analytics report of your blog's traffic and say, "Here's hard proof that people will respond to this story. Look at all these readers and comments."