I am by no means an expert, mechanically, to preface this. I speak purely from my experience with the class when I say this.
Without another person to assist you in engaging in PvP, completing contracts on your own as an assassin is very difficult. You could say 'skill issue' or something reductive along those lines, but I know how to corner stealth, I know how to flatfoot people in a variety of ways, I have a very keen awareness of how sneak/death attack works in the rolls and how to counteract high AC and everything along those lines. Still, it's not enough.
Simply put, assassins cannot operate on their own 90% of the time. I feel like a single mechanical change could change this, among those I'm presenting here. Any one of them would make assassins far more capable of doing what they're supposed to do.
Hide in Plain Sight
HIPS, especially for a class as in-tune with illusion and/or concealment (see Improved Invisibility/Invisibility on cooldown) would be an excellent way to make the class that much more powerful and independent, while being completely in line with the roleplay.
Assassinate buff
This sounds a little ridiculous as it already provides about 25-27 damage per hit that goes through all immunities etc. I believe Assassinate, being a 10 minute/PC target ability, would not be that overpowered for the change I'm proposing.
If mechanically possible, I feel assassinate should make the target flat-footed. This would make it very difficult to fight an assassin who has literally studied how to murder you face-to-face. You would need back-up or you would need to just run away.
Grenades
This was already suggested, but it's quite a simple change so I'm presenting it anyway. Rogue grenades for assassins, or at least scaling choking powder, would be an incredible change. Assassins are very familiar with poisons, so being able to stand in their choking powder while making it more effective (increased DC) would be completely in line with their mastery over poison that already exists as a class feature.
A new ability entirely?
Something like a WoW rogue's Shadowstep, where it teleports you near a target within a certain range and gives you movement speed, invisibility, or both. That would be very useful. Even something like this providing a momentary advantage would go miles in making the assassin class a little more independent.
All in all, I think assassins, for all their fascinating roleplay, mostly have to collaborate these days to see someone dead. These potential changes would make that so much easier, and people wouldn't be wasting money on placing or paying off contracts that don't get done half the time.
A little more stricter enforcement of the "no freelancing" rule, like helping factions kill players, even unpaid, might help make these changes a little more balanced too. For the expectations an assassin has, I don't really think they have the ability to see most of the contracts I've seen through. As a player, this has been very frustrating for me.