How does the service module work?
According to the documentation the URLs shouldn't necessarily have .json at the end, but I guess this is a setting you've changed if it's working for the node functions. I know you're not going to like this answer (I'm fairly certain you've tried it before) but the URL is: mydomain.com/service/rest/taxonomy_vocabulary/getTree. I've even been through the service and rest_server modules' respective code and that is definitely what it should be.

For further proof look at the (valid, passed) test module for services taxonomy_vocabulary:

ServicesResourceTaxonomyTests::testVocabularyGetTree.

You'll see that the URLs accessed by this successfully passed test are: $path . '/taxonomy_vocabulary/getTree', where $path is the path to the endpoint (i.e. mymodule.com/service/rest/).

It really would help if you could provide a live link though so we can test to see if the problem is in your Java code or with Drupal (although the latter seems very unlikely).

EDIT

p.s. do comment on this answer as I have a lot of experience with the services module and I'm sure I can point you in the right direction with a bit more info. It pains me to see someone struggling with something that I've had nothing but joy with in the past!

ANOTHER EDIT

This is the response I get from http://delvelogic.com/merchant/drupal-6.22/services/rest/taxonomy_vocabulary:

&lt;?xml version="1.0" encoding="utf-8"?&gt;
  &lt;result&gt;
    &lt;nodes/&gt;
    &lt;module&gt;taxonomy&lt;/module&gt;
    &lt;name&gt;&lt;/name&gt;
    &lt;help&gt;&lt;/help&gt;
    &lt;relations&gt;0&lt;/relations&gt;
    &lt;hierarchy&gt;0&lt;/hierarchy&gt;
    &lt;multiple&gt;0&lt;/multiple&gt;
    &lt;required&gt;0&lt;/required&gt;
    &lt;tags&gt;0&lt;/tags&gt;
    &lt;weight&gt;0&lt;/weight&gt;
    &lt;vid&gt;4&lt;/vid&gt;
  &lt;/result&gt;


Notice the &lt;vid&gt;4&lt;/vid&gt; bit...I'm pretty sure the vid you should be looking for is 4, not 1!