Well, my 03 Eclipse owners manual has a section in it on how to do it!

1. ground pin 1 of the data connector
2. insert the key in the ignition
3. press hazard switch 6 times in 10 seconds (door locks should lock and
unlock, indicating your in program mode)
4.press the transmitter switch once, then again two more times within 10
seconds of the first press.  I'm reading it from the book,  I would guess
three times in a row would work too.
5. confirmation of programming complete is, doors will lock then unlock
again
Note that you must do this with ALL your transmitters, EVERY time you
program a new transmitter.
You have 1 minute between transmitters, or the codes will be cancelled.  You
can only enter 4 different transmitters, (start at step 4, for the second
transmitter).

Note that this procedure applies to an 2003 Eclipse, I suspect its the say
for you, but no guarantees.
Let us know if it works

Nirodac