Writing/journalism/research/proofreading/copy-editing/indexing that you do freelance from home fits the bill (I don't want to say exactly what I do as it might identify me). You can train in a lot of these things, proofreading for example, quite quickly.
I work for £17 an hour with one of my clients and that is considered a shamefully low rate in my industry (I accept it because they give me long-term, regular work). For other clients I usually work on contracts with fixed fees. They tend to work out to about £200/day. Overall, I can make about £25K for a 3-day week (if all goes well, obviously there are times when I haven't got much work on, but I'm usually busy).
Out of that I do have to pay for things like reference books, computing equipment, pay my own pension and of course I don't get sick pay or holiday pay etc. But it's still very well paid and working from home is heaven.
I work 3 days a week and DS goes to nursery on those days. It would work equally well doing a 5-day week just working in school hours.