Conditions:
1. Cleared the Radio Tower- This unlocks the ability to rematch trainers through pokegear.
2. Aquire the Amulet Coin- Found in the basement of Goldenrod Department Store.
Method:
Set your DS clock to Tuesday 10:00 PM
In the Olivine Lighthouse, you will find Gentleman Alfred (1F, first trainer you see when you go up the stairs). He only has 1 Pokemon (a Level 36 Noctowl) and gives 14400 Pokedollars upon being defeated.
If you don't have his number, simply go talk to him and he'll offer it again.
Call him to arrange a rematch and simply defeat his weak (for that point in the game) Noctowl. If you have an Amulet Coin equipped, he will give out 14400 money.
Remember that you can't call a trainer if you are in the same location as them. Thankfully different floors of the lighthouse count as seperate locations, and Alfred is conveniently standing right next to the stairs.
He gives one of the highest prizes as the reward increases after entering the Hall of Fame then again after beating Red
The rest of the answer is for others that have already gone through the league so ignore it if you haven't beaten the game.
For anyone who has beaten the league (or even red) this is still the best way in my opinion. While other trainers give more money (e.g. All gym leader rematches before you beat Red, Lance etc.), this battle is the fastest. You can repeatedly challenge the Elite Four which earns a lot more money, but it is still worse for 2 reasons-
- The battle with Alfred is against 1 relatively weak Pokemon. In the league though you have to fight 5 powerful trainers with 5 or 6 Pokemon each. In the time it takes for you to beat the league, you could have taken out Alfred at least 10 times.
- Every time you enter the Hall of Fame, there is an extremely long cutscene and end credits. Meanwhile all you need to do to rebattle Alfred is go downstairs and make a phone call.
Gym leader rematches are also a good way to make money (they also give a ton of exp), but run into the first issue as well; 5 strong Pokemon vs 1 weak Pokemon.
Red gives the most money upon losing but he is also the strongest by a mile. Plus to rematch him, you have to beat the stronger Elite Four and climb Mt. Silver. It also means sitting through the end credits twice.