I'm not very familiar with Eberron. Unless your DM has some special goblin-related things developed for the campaign, I would expect this would be a reasonable request. The goblin's bonuses don't jump out at me as being unbalanced:
GOBLINS AS CHARACTERS
Goblin characters possess the following racial traits.
— –2 Strength, +2 Dexterity, –2 Charisma.
—Small size: +1 bonus to Armor Class, +1 bonus on attack rolls, +4 bonus on Hide checks, –4 penalty on grapple checks, lifting and carrying limits 3/4 those of Medium characters.
—A goblin's base land speed is 30 feet.
—Darkvision out to 60 feet.
— +4 racial bonus on Move Silently and Ride checks.
—Automatic Languages: Common, Goblin. Bonus Languages: Draconic, Elven, Giant, Gnoll, Orc.
—Favored Class: Rogue.
They are indeed small, so they have to use the small-sized weapons.
The closest races from the PHB would be halfling or gnome. The goblin is taking an extra -2 stat penalty compared to either of them. The biggest benefits the goblin gets in return are the 30' base movement (nice, but not unbalancing) and the Darkvision 60' (similar to a dwarf or half-orc). The +4 bonus on move silent and ride are probably about equal to the bonuses that the halfling or gnome get.
Since I primarily DM, my main experience with goblin characters has been NPCs. I've made a few goblin rogues before. What works for other small-sized rogues works for them:
- Small-size adds a big +4 bonus on hide in shadows and goblins also get a +4 move silent bonus. Use that to your advantage and try to sneak around to stay out of harms way and take advantage of sneak attacks.
- Small-size means their base damage is smaller than usual. In addition, critical hits are less important for small-sized characters. They tend to have lower strength (-2 str penalty for the goblin) and the weapon damage is lower as well. But none of that impacts the sneak attack dice (xd6). When attacking, it's even more important for small-sized rogues to try to catch opponents flat-footed (via high init or stealth) or flank them than it is for larger rogues. Good feats are Improved Init as well as the Dodge/Mobility route to let you move into position.
- Small-size characters tend to have much higher dex than str, so Weapon Finesse is usually very useful.
- Two Weapon fighting lets you get more attacks, and possibly more sneak attacks.
Given those, the general feat track I'd recommend for a small-sized rogue would be Improved Init (1st), Weapon Finesse (3rd), Two-Weapon Fighting (6th). Wait to take Weapon Focus only after you've decided on a decent weapon (or weapons). You never know what your DM might hand out. It would suck to choose rapier and then find a small-size short sword of ultra-buttkicking later on. Another feat to consider is Improved Toughness if your DM allows feats from Complete Warrior. It can be a great feat for lower hp types like rogues. Dodge & Mobility are useful as well.
Rogues don't get a lot of feats, so if you like the rough&tumble up close style, you may want to consider multiclassing to fighter for a couple levels to pick up a few extra feats as well as gain martial weapon access and some larger HD. However, the pure-rogue build will always have more skills, higher sneak damage, and reach the other upper rogue-level abilities faster.
The skills I'd concentrate on would be Move Silent, Hide in Shadows, Tumble, Climb, Spot, Listen, Search and Bluff (to rehide). If you have enough intelligence to learn more, then pick up some ranks in Pick pocket, Open Lock, Disable Device and so forth. With the charisma penalty, the other social skills (gather info, diplomacy, etc) are probably going to be poor for a goblin, but could certainly be useful for infiltrating humanoid groups to learn info, so it's your call on whether to dump points into them.