I recently bought a 2002 with low mileage, and I need to charge the battery.  I bought a charger from a motorcycle store.  The charger comes with the regular alligator clips as one option, and it also has cables that connect permanently to the battery.  This uses a sort of quick-connect and I guess you leave the cable inside of the bike’s side covers.  I have not had it apart yet.

But there’s one thing I don’t understand.  I have the Suzuki service manual, and it says that you should never charge the battery while it in the bike.  But I wanted to trickle charge the battery all of the time since I only ride only or two days per week.  The charger says it is specifically made for this use.

So my questions are 1) will it hurt the electrical components of the bike if I charge the battery in place, and 2)  is it OK to trickle charge all of the time?

If I have to take the battery out of the bike every time I need to charge it that will be a hassle.  I have already found out that the battery has to be “up” in order to crank the engine.  A marginal battery does not seem to be adequate for this engine.

Does anyone have any advice?

You should be fine charging the battery while on the bike. I've been using a trickle charger on my '02 for over a year with no problems. All I did was install a pigtail on the positive lead of the battery and used a 1/2 amp 12 volt power supply that came from Radio Shack. I'm guessing that Suzuki doesn't want the battery charged on the bike in case it blows up. That can happen if you try to overcharge the battery using a high amperage charger. Keep the amps low with a long charge time and you will be fine. There is a formula to determine the proper charge rate for a battery but I've forgotten it,  maybe someone out there knows it.  Ride Safe, Ed L.

I have a 96 i bought used and the previous owner put in a new battery for me.  It sat from Nov. to March about 4 months without starting it and the battery in the bike.  I went out and fired it up no problem.  Why are your batteries draining so quickly???  I'd think a battery should hold a charge for a week.  If not I'd spend the money on a new battery and not a trickle charger.

Yeah, the only time I've used mine was when I turned the key the wrong way and left the taillight on overnight.

Trickle charger won't hurt it. I've jumped off mine a couple times with an 825 amp truck battery with no problems. I had a Savage battery last 5 years...with winter trickle charge and weekly riding in warm weather.
-WD

Don't forget that a big part of the manuals are written with a concern for lawsuits and warranties/ otherwise nobody will remind You that the gas is flammable/.  Suzuki is just covering all the bases to make sure to lower down the risk of any kind of misshaps.
Don't worry. The best thing You can do is to attach a nice fat wire to the "+" terminal and use it for charging or for jump.  When not in use- just cover the end with wire nut.  For ground You can use any metal part of the bike /the best is the cylinder/. All the automotive chargers have 1 or 2 amp setting and 90% of the chargers are automatic, so You will not overcharge the battery.
The only down side of charging the battery on the bike that I can think of  is that the corosive fumes will be around the bike.