I'm playing Soul Silver and I'm trying to get an Umbreon but it's taking forever...any advice?
Short answer: Walk a long time, or feed it lots of tomatoes.
Eevee has a base friendship value of 70. Taking a look at a list of known ways to increase friendship on the same wiki site, you'll observe that the simplest way of doing so is by walking in this generation.
With every 128 steps you walk, the game flips a coin. If you win, every monster in your party gains 1 friendship point. After 150 points, Eevee will have 220 and can evolve when levelling up.
You would need to walk an average of 38400 steps to evolve your Eevee. The exact amount will follow a binomial distribution.
Alternatively, you could use items, but that can become expensive. The cheapest way is using the friendship berries1. To go from 70 to 220 requires you to use 33 of them.
1: These include the Pomeg Berry, Kelpsy Berry, Qualot Berry, Hondew Berry, Grepa Berry, and Tamato Berry (#21 through #26).
According to many articles on the internet it is recommended that you do the following;
Soothe bell to get happiness up.... Make sure you level at night for umbreon and day for espeon... Best advice is don't let them faint... and be patient. Hair cuts and soothe bells help a lot.
And another source for confirmation:
Getting an Espeon or Umbreon in HG/SS is mostly the same as in G/S/C, except that the time-of-day durations are the same as in D/P/Pt, and the Soothe Bell and EV-lowering berries are yet again available.