The list of ways to make money with a conlang is short, so step one is to be creative.
Write Genre Fiction Books.
Authors do make a living writing and selling books, sometimes with an artificial language bundled with it. Wardesan, Láadan, Tolkien's books are good examples. I'm guessing the conlang part though is reducing their income, they could write more books if they skipped writing a conlang. Personally, I'd buy a book with a conlang if the author tried to make it simple enough to enjoy for 10 to 20 hours. Instead we get unusable languages that require 2000 hours of study to appreciate them, same or worse than a natural language. And I'm an outlier, so I'd imagine regular genre fiction buyers see a bundled language as a low value gimmick.
Communication Systems for the Disabled.
Blissymbols made money, albeit in a rather dishonorable way by suing the institution that was trying to help the profoundly disabled communicate with a symbol board, which was in essence an artificial language. I spoke with a specialist in the more modern versions of these, and often vendors don't even bother to acknowledge that symbol boards are not English, but conlang-like systems with all the challenges.
In the realm of conscripts, there is a commercial writing system for ASL. I'm failing to re-find the link.
Historical BSL was essentially a franchise and BSL was something of a trade secret.
Movies have been hiring professional linguists (Klingon, Na'vi) The Klingon dictionary and Avatar handbook sold a lot of copies, but the authors both became professional linguists first, and these books are really side projects.
Selling learning materials.
This has got to be the worst way to monetize a conlang. The artificial language section of any large library has to be littered with books of people who thought they could sell a lot of copies of their grammar summaries, workbooks and dictionaries. No one wants the grammar summary. What they want is to meet their significant other by learning a language which brings me to...
Esperanto actually has economic activity, but the language is already written. Building a language starts with grammar and vocabulary, but to extract money from people, people need to learn it. If your interest in conlang building is in the community building part, then it might make more sense to make a living working with an existing conlang that has attracted a community, complete with conferences, etc. That said, I'm guessing no one is getting rich off of Esperanto, but there are teachers of Esperanto, etc.
There have been reports of people writing full languages for computer games, card games. Magic the Gathering's Phyrexian comes to mind. So far, these have been gimmicks and the amount of money, I'm guessing is not a lot. Some of the game makers don't even bother to publish the grammar and dictionary! This makes it sort of into a laborious game of decipherment.