avoid the verb say when you have a lengthy conversation

You don't always need a dialog tag. Also, by convention, a new speaker means a new paragraph. Your passage might read like this:

Jack poured some coffee. "I can't do it." He cleaned the glass. "I may resign tomorrow," he said, taking off his jacket. "I want to talk to my boss tomorrow."

"Don't quit Jack," said John.

"I don't have an option. I can't work there anymore."

I don't think it's necessary to avoid "said." Despite claims it gets repetitive, imagine how much more distracting it would be to the reader if a writer dug deep into the tag bucker and used "remarked," "stated," "claimed," etc.

But if you did want to avoid it, you could leave off the tag entirely (I think this below is termed an "action tag"):

Jack poured some coffee. "I can't do it." He cleaned the glass. "I may resign tomorrow." He took off his jacket. "I want to talk to my boss tomorrow."
"Don't quit, Jack," said John.
"I don't have an option. I can't work there anymore."

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Actually, I was much more distracted by the insertion of the actions of cleaning the glass, etc. than by your use of said. It puts too much info in my head and distracts from the conversation, and the convo seems to be the point of the scene. Is there a reason the actions are there? I used to add all sorts of action to make it seem more real, but today I don't believe it's necessary.

Jack poured some coffee. "I can't do it," he said. "I may resign tomorrow. I want to talk to my boss tomorrow."
"Don't quit, Jack," said John.
"I don't have an option. I can't work there anymore."

Click to expand...

If this 'lengthy' conversation is between two people you need careful word choice so the dialogue flows back and forth.

And if there is only two people the word 'said' does become redundant because it should be obvious who spoke.

There's no need to bulk things up with pointless actions.

The focus should be on the content of the dialogue and the actions/reactions of each character to that dialogue.

1. When it's clear who's speaking, you can omit the speech tag entirely. (I assume your example is all run together in a single paragraph because it's just illustrating multiple "said's." In an actual piece of fiction it would be three paragraphs. And most of the speech tags would be completely unnecessary.)
2. You can replace a speech tag with an action on the part of the speaker.
3. Don't sweat it. "he/she said" is pretty much invisible to readers.

As others have said, speech tags like said and asked are pretty invisible to a reader, so I wouldn't worry too much about those.

That being said, you can get away with them for a few dialogue exchanges if it's clear who's speaking, especially in a two person conversation.

I like to go back and forth between tags and no-tags in my dialogue to control the pace of the story.

Something like this:

"How's the new job going?" Rosa asked.

"Pretty good actually," said Maria.

"So you didn't end up with the creepy boss?"

"No, I got into the accounts payable division. The company is so big we never even talk to receivables."

"That's great! I bet your daughter loves your shorter commute." Rosa said.

Maria got up from the table and washed her tea cup out, slowly working a cloth across the porcelain. "Actually, she's not talking to me at all."

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This way I don't have to say that Maria paused, or is upset, the reader can infer that and the tone of the conversation slows way down when she gets up to wash her cup.

I would far prefer writers use "said" as a dialogue tag, instead of things like "avowed", "insisted", "complained", etc, since the former almost becomes akin to a punctuation mark and disappears into the seamless reading experience. Having ... er... said that, however, "said" being continuously repeated from one dialogue tag to the next does become distracting and would drag this reader out of the narrative.

As mentioned upthread, be sparing with the number of dialogue tags you use and employ them only where the reader would otherwise not know who is speaking. Dialogue tags may be replaced with action beats, but I would be careful how you use them, too. IMHO they also need to earn their corn and should have more of a pupose -- like showing character for example -- than merely indicating who is speaking.

Who is your favourite author? Pull out a story by them and examine the text to see how they do it.