Doesn't sound like it should be too hard to code if there's not an existing solution out there already. Here's an idea though - if you can find a generic tumblr poster that lets you schedule posts, maybe it'd be easier to make a simple tool to read a CSV and output it to articles that can be read by that poster? Just something that came to mind...
(I know nothing about tumblr I'll admit, but have a lot of experience automating posting on various sites...)