OK, without spending a ton of money for a wonderful (and pricey) set of new gears for my transfer case, what is the cheapest way to get a little bit lower gear ratio to accomodate the 31.5" tires on my '87 Suzuki?  (I would really rather save the money for a coil spring suspension kit.)

put it in low range, you would turn 3,844 rpm's at 55 mph.

OK let me be more specific.  My Samurai has the stock drivetrain (tires excluded).  I want to lower the gear ratio overall to accomodate the 31.5" tires which it now has by changing one or more parts in the drivetrain (i.e., differential part, tranny part, transfer case part) while spending a minimal amount of money on those part(s), and no, I don't want to drive around in 4 wheel low all the time to accomplish this.  Any suggestions?

This is listed in "cost sequence"

Probaby transfer case from an SJ140 if you can find one in a salvage yard.

Sidekick/Tracker 4.63 differential gears from a salvage yard. On 31's you'll be about 10% under stock, makes 5th gear useable. You'll need two front 3rds from trackers with automatic transmission. Search the faqs for details

If you have to pay someone to setup up the 3rd members, 4.1 tcase case gears are cheaper.  about 400 US. (in the long run you'll be happiest with the tcase gears.)

And I can find 4.1 T-case gears for $400. where?

Trail tough sells them and ships anywhere in the world, they also have thier 4.9 gears on sale for like 535.00, get on thier web site and check them out.

Check the faqs for what you will need from the donor vehicles.
Browse an online factory service manual for how to setup a 3rd.

I've only set up one front 3rd, and it was the fussiest touchiest thing I've done on my samurai.  Hope I don't need to do it again.

Some of the tools are a bit pricey, like a torque wrench that reads accurately in low inch/lb ranges.

  You know, if you wanna go coils and spend your dough there, you can just drive the Sammi stock with the 31's on it.  It won't be the fastest thing in the world and be careful not to fry your clutch, but you'll be ok.  I made a full day's wheeling at fall Zuwharrie 2004 with 33's and a 1.3 with stock gears. 
  Also, you can search this site for the term "hybrid rear" this is a mod that allows you to put Kick gears in a sammi.  To make a long story short, the Kick's came with a variety of gears depending on year, engine, doors, and transmission.  If I'm not mistaken the lowest gear ratio was a 5.something in a 4dr 1.3 stick Tracker.  But, these third members don't just slide into a sammi, the carrier is wrong.  There's some cutting and welding involved.  Search the site, if you don't find the proper info, then ask around, but this is a good thing for you to do either now, or after you spend your bucks on a coil setup.

you can come across tracker/sidekick diff gears sometimes for a decent price... I have 4.62's going in this coming sat.  I paid 75.00 for one set, and traded a older extra softtop I had for the other...

check local yards for them, also browse suzuki forums online for them... ebay sometimes has them up. some are asking to much for them, but others are ok priced.

 
Also, you can search this site for the term "hybrid rear" this is a mod that allows you to put Kick gears in a sammi.  To make a long story short, the Kick's came with a variety of gears depending on year, engine, doors, and transmission.  If I'm not mistaken the lowest gear ratio was a 5.something in a 4dr 1.3 stick Tracker.  But, these third members don't just slide into a sammi, the carrier is wrong.  There's some cutting and welding involved.

Let me try to clear some of this up.....
You don't have to use a hybrid rear axle to run trackick gears in a samurai.  FRONT trackick gears will work in both the front AND rear axle of a samurai.  Trackick front gears (with 22 spline sidegears) are a bolt in into a samurai front axle (the pinion flange may need to be redrilled to mate up to your driveshaft).  Some trackick front gears (the ones that have 26 spline sidegears) will bolt into the rear samurai axle (may need to drill the pinion flange, as mentioned above), otherwise, the samurai sidegears will need to be swapped into the trackick carrier OR the trackick gears can be swapped over to the samurai carrier and housing using a "can and shim" kit from one of the vendors.

The lowest gears that came factory in a sidekick were the 5.62s that came in ONLY the 1989 sidekicks that had 1.3 CARB engines in them (BTW, not all 89 sidekicks were carbed, some did have the 1.6 EFI engine).  Again, if you can find 2 FRONT gearsets they will bolt in with minimal mods.
The only cutting and welding that is required to swap trackick gears into a samurai is if you want to use trackick rear gears in a samurai.  To do that you will need a hybrid rear.  A hybrid rear is a trackick center section with samurai axle tubes on it.  You use the complete trackick center section and thirdmember, gears etc and the samurai axle tubes, shafts, brakes, etc.
The most common gears you will find in trackicks are 4.625s and 5.125s.  IIRC, there are some that have 4.30s (but these are mainly found in canada, I believe).

Hey Skyhiranger. I really liked all the info you put into the last message. I am looking to go even lower in my sami. I currently have RRO Megacrawlers. I am becoming a gear-addict. So, front and rear I can put front 3rds from a sidekick or tracker? What should I expect to pay for a pair? By the way... I ran the rearseat for awhile... decided it was hurting my cool points and taking up valuable space, so I took it out and now have cool points again!!!!

Sent you a PM.

Yes, trackick front gears will fit both samurai axles.

At least the seat is easy to remove...2 pins and it's gone.