1993 lebaron relay problems

1993 chrysler lebaron fuel pump relay fuses keep blowing. New pump in and continues to blow fuses. Will run for awhile then stutter.

I had a similar problem and it was the plug that connected to the fuel pump. The insulation on the wires gets old and breaks off in places where exposed to the elements like the fuel pump plug [or by a heat sourse (I also had a problem with another issue by the engine, a connector plug short)]. It may be hard to see but I would take a good look at that plug first.
Nick