Here's a summary of the best races for winning cash. The times I give are actual elapsed times in B-spec mode (except for Capri) and are close approximations since they'll vary depending on the car used. The times also assume that in the case of enduros the game is reset to 3X speed immediately after all pit stops.
Deutsche Touring Car Meisterschaft (DTM)
Prize money: 150,000
Prize car: Mercedes Benz CLK-GTR race car
Car value: 743,749
Total cash: 893,749
Time: 16 minutes
Credits per minute: 56,000
Advantages: Fastest payoff rate in the game by a wide margin.
Disadvantages: Takes seven game days. If Day 694 is right around the corner and you have your eye on the black beauties, you might want to consider the Nurb or Fuji races instead, at 3 game days each. Requires a decent B-spec driver.
Capri Rally (Easy) at Costa di Amalfi
Prize money: 10,000
Prize car: Toyota RSC rally raid car
Car value: 265,624
Total cash: 275,624
Time: 9 minutes
Credits per minute: 30,000
Advantages: Fastest race to run. Available right at game start, provided you started the game by earning the IA license and have the Nismo 270R prize car from it. Best for a quick shot of cash to buy most production cars and tuning parts, unless the production car you have in mind is something like a Shelby 427 Cobra.
Disadvantages: Must be driven A-spec; B-spec not available in the Special Conditions hall. Requires National A license.
El Capitan 200 Miles enduro
Prize money: 250,000
Prize car: Toyota Minolta 88C-V race car
Car value: 743,749
Total cash: 993,749
Time: 43 minutes
Credits per minute: 23,000
Advantages: Pays more than DTM and in fewer game days. Fastest enduro payoff.
Disadvantages: Still takes twice as long as the DTM. Endurance events require 25% game completion.
Fuji 1000 km
Prize money: 750,000
Prize car: Nissan R92CP
Car value: 743,749
Total cash: 1,493,749
Time: 2 hours
Credits per minute: 13,600
Advantages: Lots of cash in a reasonable amount of time. Best race to run unattended; ideally suited to leave running overnight making money while you sleep, or leave running while you're at work/school.
Disadvantages: Requires a top grade properly tuned LMP car to win, or the Formula Gran Turismo. Endurance events require 25% game completion.
Nurburgring 24 Hours
Prize money: 1,200,000
Prize car: Formula Gran Turismo
Car value: 1,593,749
Total cash: 2,793,749
Time: 9 hours
Credits per minute: 5,200
Advantages: Best payoff per game day. A single race can pay for two of the week 100 black beauties, the R92CP and Mazda 787B.
Disadvantages: Takes the longest to run. Endurance events require 25% game completion.
The Japan Championship takes about as long to run as the DTM and only pays 391,249.
Schwarzwald Liga B also takes the same time as the DTM and only pays 421,874.
The All Japan GT Championship at 10 races takes much longer than the DTM and only pays 536,874.
All other events in the game, with one exception, pay even less except for some other Special Conditions Hall events, but they're in the same ballpark as the Capri Rally.
The exception is the highest paying event in the game, the Formula GT series. It pays 4.5 million in cash prizes alone. However since it's 15 full blown enduros, I don't think anyone would consider it as a quick cash maker.