There's a great variant for two here on BGG:
Starfarers 2-player - tweaked and tested.
The variant has been tweaked and tested to give two players a "full game" feeling. There's no large part of the board left unused. There's no awkward playing of two colors per player. If I may say so, it's the best two-player Starfarer variant you'll find in this part of the galaxy.
What you do: Play as normal except as indicated.
Each player may build only once on any given Catanian Colony. After the game begins, no more colonies may be built on the Catanian Colonies. (To be clear, there can be two colonies on any given CC, they just have to be different colors).
Turn three cards face up from the reserve pile to form a Trading Trio. These cards will be available for trade later on.
Changes in play:
Each player may build only once on any "outer" planetary system.
During trading, a player may opt to trade a card for a card in the Trading Trio.
He takes the Trade Trio card and leaves his own in its place. He may do this once per round.
Players may also freely trade with each other.
At the end of player's turn, the #3 card in the Trade Trio is discarded, and a new card is drawn from the reserve pile to become the #1 card (the other cards slide over to new positions). If the reserve is depleted, shuffle the discards and start a new reserve with those.
To build a trading outpost, a player's ship must have 1 freight ring plus 1 freight ring for every trading post already built anywhere (Maximum of 5 freight rings). So if there's an outpost on the Diplomats, two outposts on the Green Folk, a player would need 4 freight rings to build another trading post anywhere.
Play to 20 points
Given that a player can place 9 colonies, 3 spaceports, and will on average gain 2 Friendship rings, he will still be 4 points short of the 20 points needed to win the game. Players must make up the difference in fame points, defeating Pirate lairs and Ice Planets, or stealing Friendship rings from the other player. So plan ahead! If you find yourself with only one ship left and lacking points, don't turn that ship into a colony or an outpost until you can make up the difference.
Since each player can only build once on each planet system, players will have to visit the far ends of the board to get their points.
7 rule: We use this rule in all our games. If you role a 7, take tribute and steal a card as normal, and then that player rolls again. If it's a 7, move on. If it's any other number, collect resources as normal. It makes the game go faster and more fun.
We use this when we want to play two player - there is another one - check out the game page: