He's negative credit income because his planets are underdeveloped, not because his fleet logistics are upgraded. Fleet size upgrades simply reduce the amount of income you get, they can't force you into the negatives. The only thing that can force you is the underdevelopment tax that is in effect on a freshly colonized planet.
To the OP I suggest that he try to do two civilian population upgrades to every planet you colonize as soon as possible. Ideally you can do this the moment you colonize the planet. This may not give you much of an income boost or total income depeding on your fleet costs, but you should at least not be in the negatives. In your situation, my strategy would be to focus on planet upgrades over the next little while to correct the negative income problem. You could also look into setting up one (or more) trade ports at each of your planets. Since you have negative income, unless you can sell metal/crystal to generate the income needed you may have to scuttle the planets giving you the largest penalties and wait to recolonize once you can afford the civilian upgrades when you retake them. It would also probably be helpful to take some of the pressure off yourself from the AI. Since I assume you have a superior fleet, attacking his planets, particularly his home planet if you can get to it, will draw his fleet away and possibly give you some breathing room to get your empire back in order.
Of course, if the AI is in full economic and build boom mode, this may not be possible at your point in the game but you won't know until you try.
-dolynick