Fully charge your battery before doing any testsTest your new battery's voltage after a fresh charge and then hit the starter for a few seconds and check it again. A big voltage drop to 12 volts or below indicates you new battery may be dropping a cell. Take it out and have it load tested at Advanced Auto or Autozone.
if battery is good, roll on to the charging system.
===================================
You can bench test your regulator rectifier with a volt ohm meterLooks like this:
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1245984387/3#3You can live test your stator, method is page 210-211 in Clymers
===================================
Once you are happy and content that your Regulator Rectifier is rectumfried, go get another one cheap on Ebay.
http://www.ebay.com/itm/07-Suzuki-S40-Boulevard-LS650-REGULATOR-RECTIFIER-/13...http://www.ebay.com/itm/Suzuki-Boulevard-LS650-S40-Voltage-Regulator-Rectifie...You will want to check your stator output of course (they rarely go bad), but most likely your issue is a bad regulator rectifier.
The one on top looks better and costs a dollar less.