I believe TC 8.x and TC 9.x REST APIs are pretty similar. This example was written for TC 9.x.
I don't know if you have sorted this out, but (for the record) you have to do what the "Create a new build configuration with all settings" says. Basically, you have to create an XML with a format like this:
<buildType id="YourBuildID" name="YourBuildName" projectId="TheProjectIDThatOwnsThis" >
<project id="TheProjectIDThatOwnsThis" name="TheProjectName" parentProjectId="TheProjectParent" href="TheProjectHREFValue" webUrl="TheWebURLOfTheProejct"
/>
<template id="TemplateID" name="TemplateName" templateFlag="true" projectName="ProjectThatHasTheTemplate" projectId="ProjectThatHasTheTemplate" href="TemplateHRef" />
<vcs-root-entries>
<!--vcs-root-entry elements are not necessary-->
</vcs-root-entries>
<settings>
</settings>
<parameters>
</parameters>
<steps>
</steps>
<features>
</features>
<triggers>
</triggers>
<snapshot-dependencies/>
<artifact-dependencies/>
<agent-requirements/>
<builds href="BuildConfigurationHREF" />
</buildType>
And do a POST to this URL: http://TCServerName:Port/httpAuth/app/rest/buildTypes
That is the XML expected by TeamCity, so it's up to you in which programming language you will create it. I have done this with C#/LINQ to XML and worked just fine.
Hope this helps.