Visual mapping software can help with organization if your child is a visual-spatial kind of person.
The outlining functions in your regular word processor can be useful, too, for setting up the initial organization of the writing piece.
It might be helpful for your child to remember the acronym "POWER" - Plan, Organize, Write, Edit, Revise - even for small writing assignments.
The "Plan" part is essentially narrowing down the topic, the audience, and the purpose. It can be developed by asking questions: "What am I going to talk about?"; "Who am I talking to?"; and "Why do I want them to know?". In the case of persuasive writing, questions like "What is my position on this?" and "What do I want the reader to do as a result?" can be helpful here.
Even a single word at the top of the page answering each of these questions can be very useful for helping the writer keep focused on the topic, audience, and purpose, which greatly increases the likelihood of developing an appropriate piece of writing.
"Organize" is where the visual mapping software or outline function really can make a difference. The writer can choose a single keyword or phrase that best communicates the choice of main topic, and put that either in the chief space of the graphic organizer or the first level of the outline. This word will become the theme of the essay, or the main idea of the paragraph, or the subject of the sentence, depending on what level of complexity you want to start at. Next, the writer brainstorms at least 3 to 5 single words or phrases that relate directly to the topic and add detail, support, or elaboration. He or she should then decide which 3 or 4 of these words will best help someone from the intended audience understand more about the topic. These words will go into the graphic organizer below the main keyword or into the outline at the second level and will eventually become either the main ideas of paragraphs in the essay, the supporting sentences in a paragraph, or the details in a sentence. If the writer is working at the sentence level, he or she can stop here and go on to the next step. If a larger piece is in the works, the writer can then take each of these words and choose three or four words which expand, elaborate, or add detail, and fill them in below the second-level words. This process can be repeated as many levels as necessary to plan out the structure of the writing all the way from overarching theme down to sentence details, if needed.
With practice, this part can go very fast. When I was first working with my son with this, I would give him prompts and the only output I would ask for was the plan and the organization. Once he was fluent with the brainstorming part, we moved on to the rest of the writing process.
If your child has had a lot of discouragement already about writing, I'd start at the level of the sentence, which is quick and manageable, and has the potential to give some rapid success without much effort or task commitment, and then once there is some confidence around the ability to produce clear, detailed sentences, you can move up to paragraphs and essays just by adding successive levels of iteration.
The "Write" step takes the organizer map or outline and expands each of the keywords into a detail, sentence, paragraph, or essay, depending on what level in the organizational map it falls and what the desired end product is.
The "Edit" step checks for errors, such as omitted words or letters, punctuation, spelling, grammar, etc.
The "Revise" step consists of reading through the draft and deciding if it is clear, if it sticks to the topic, and if it is as effective as the writer can reasonably make it within the constraints of time and length allowed. (I actually think that this step should come before the "Edit" step, because I can't see the point in correcting the punctuation in a sentence or paragraph that is going to be rewritten anyway, but then that would mess up the acronym, I guess.)
I'm sorry I don't have any visual mapping software recommendations: my son encountered graphic organizers once, and begged me to never make him use anything remotely like that again, as it was extremely confusing for him visually, so he just uses outlining and it works for him.
HTH
