I think I'm going to try a set of polyurethane bushings.
Such as from JC Whitney or some other source.

I've had this same "bed spring noise" from the front of my 2004 Mercury Mountaineer AWD V8 since the day I bought it (used), it has about 40k miles on it now. When ever I go over a bump or the front suspension gets loaded and unloaded I gets this squeaky noise. I thought it was coming from the front springs however after reading this thread I'm sure its the sway bar bushings. What tipped me off was when Dayhike posted the lubricant solution.

However I would not spray lubricants on rubber suspension parts.
When I was a kid I was pumping gas at this gas station and I use to watch the old time mechanic service cars. When ever he got a customers car up on the lift (and these were cars from the late 60's era) he would take a oil can and squirt all the front bushings under the car. I asked him why he did that and he said it got rid of the squeeks.
A few years later I was a mechanic at a car dealership and I took the oil can one day and started squirting all the rubber bushings under a car I was doing an oil change on. The mechanic next to me said "what the heck are you doing, are you nuts?". I asked him what his problem was and he told me why I should never lubricate the rubber parts like this and here is why (it makes sense): When you spray an oil on the part it tends to attract dirt, dirt and grit stick to the oil. If you have a metal part rubbing against the dirt and grit it tends to grind down the rubber or elastomer ... which wears it out quickly.

So, I'm gonna try a set of urethane bushings which are very common in most suspension upgrades.