Spontaneous encounters are rare, with a chance of 8/65536 (or 1/8192).
In a typical single time play through (all trainers, gym, elite, some wild Pokemon) of the generation 3/4 story line will yield ~2500-3500 Pokemon encountered and defeated. Which means it's highly probable for one to never encounter any alternative colour Pokemon while playing through the games.
The single most warrant way would be chaining with Pokeradar. Which yields a ~1/200 chance of an alternative colour encounter after a chain of 40.
Reseting the game is easier with 4th generation games. Due to a faulty random number generator used in the third generation games, following the same sequence will actually yield you the exact same generated number (i.e. encountered Pokemon). Thus a round of 100 reset may infact only result you 20-30 distinct Pokemon encounters, highly increasing the number of times one needs to reset for an alternative colour encounter.