Does Japan currently have a standing Army?

They call it the "Ground Self-Defense Force" so I guess the answer is no.

Here's a pamphlet from the Japanese Defense Agency: goto

Japan has supplied both naval support and troops for the Iraq War.

The Japanese Ground Defense Force is one of the largest standing armies in the world.

currently it's night time over there...I think they're lying down right now...

Article 9 of the constitution of Japan states:

"The Japanese people forever renounce war as a sovereign right of the nation and the threat or use of force as a means of settling international disputes."

This is interpreted as permitting a standing army known as the Self-Defense Forces (SDF), but has prohibited those forces from being deployed outside of Japan or possessing nuclear weapons.

Still, with nearly 240,000 military personnel and an annual budget of nearly $50 billion in 2002, Japan's military outstrips Britain's in total spending and manpower.
Source

Even with some American assistance the army still needs to modernize....

In my opinion SDA is just a concession temporarily. The new generation of Japan (including Junichiro Koizumi) will no longer tolerate their own country without essential forces and relatively poor-ranked political postion and it will ultimately lead them to seek the greater and necessary power which is desperatly needed on the regional and global stage.

Here is a little info on the Japanese Army: HERE

Links to the rst of the Japanese military: HERE