The odds of a shiny in SoulSilver are 1/8192.
What does that mean? If you roll a dice, you have a 1 in 6 chance to get the number you want. In this case, the dice you're trying to roll has 8192 sides on it, and you're trying to get one side of the 8192 sides possible.
If you roll a 6-sided dice 6 times, it does not guarantee you the number you want. You might get it on the first roll, and maybe it'll take a hundred. In this case, you might get a shiny in one egg, but maybe a thousand, or maybe even 20,000 eggs.
There is a way to increase your chances, through the Masuda Method, which changes your chances to 1/1638. Much better, but still not high.
To do the Masuda Method, you need a Pokemon from a different language game to breed with your Eevee. That may not be possible to you unless you know someone with a different language game.
For hatching eggs faster, you should have a Pokemon with Flame Body leading your party. This will reduce the amount of steps needed to hatch eggs by half.
If you no longer want to hatch eggs, you can try going to the Celadon Game Corner and exchanging 6,666 coins for an Eevee. Save the game before exchanging, and fill up your party with 5 Eevees, check if they're shiny, and reset the game if you don't get a shiny, and repeat.
Best of luck!
