It's totally up to the DM, but probably not a whole lot
The best citation I know of for this is from the Player's Handbook:
People who are able to cast spells don't fall into the category of ordinary hirelings. It might be possible to find someone willing to cast a spell in exchange for coin or favors, but it is rarely easy and no established pay rates exist. As a rule, the higher the level of the desired spell, the harder it is to find someone who can cast it and the more it costs.
Hiring someone to cast a relatively common spell of 1st or 2nd level, such as cure wounds or identify, is easy enough in a city or town, and might cost 10 to 50 gold pieces (plus the cost of any expensive material components). (PHB, Chapter 5: Equipment, Expenses, Spellcasting Services)
So the best guidance this gives in terms of an actual money value of such a service is less than 10 gold pieces. But even 9 gold pieces per casting is a lot! It's enough to finance a wealthy lifestyle with just one task every other day (also drawn from the same section of the PHB, under Lifestyle Expenses).
And, I would argue, it's too much for this service. The biggest issue is that Mending is a cantrip available to many classes (Bards, Clerics, Druids, Sorcerers, Wizards, and Artificers; more, if people want to take relevant feats).
Services that are easy to find are less expensive than rarer ones, and there is a real chance of being undercut on pricing by someone else who knows the cantrip. It's probably not realistic to think that your player's character could command 9 gold per casting-- that would mean anyone who knew that cantrip would be wealthy, which would suggest that a lot of people would make the effort to learn it. And if it's widely known then at least some people will be willing to provide the service for less.
Finally, the starting wealth for the classes with easy, automatic access to Mending is not exorbitant, which suggests that this should not be a huge moneymaker. It's as high as 5d4 * 10 gold pieces at the top for Bards and Clerics, as low as 3d4 * 10 gold pieces for Sorcerers. It's only 2d4 * 10 gold pieces for Druids, but they might not be as focused on money as other classes.
14 silver pieces to 7 gold pieces per day is reasonable as a guideline if you want variety in earnings, or 1 gold piece per day if you want it to be steady
The range is drawn from the possible outcomes listed in Xanathar's Guide to Everything (Chapter 2: Downtime Revisited, Example Downtime Activities, Work). I won't reproduce the table, but those are the extreme ranges of results. The single gold piece per day is drawn from the PHB (Chapter 8: Adventuring, Between Adventures, Downtime Activities, Practicing a Profession).
Make sure you don't let the tail wag the dog
Wealth has an odd representation in D&D 5e, and while players often enjoy earning money (especially in creative ways) their ability to do so doesn't really drive much in the game.
The only downtime the PCs will have available is what the DM explicitly grants to them. The amount of money that people have to spend on magical mending is totally up to the DM. The major determining factor in how much money a PC can make during downtime is more a function of how much money the DM wants them to have than it is a function of how valuable the PC's service is. It is entirely sensible (though definitely not necessary) for the DM to make a judgment more on that basis than on how much a real tradesperson in that setting might charge or earn.