It’s “tumblelog”. Pronounce it like the complete word “tumble” followed by the complete word “log”. No gaps, emphasis on “tum”.
The following alternatives are all wrong and awkward:
- Tumblr blog
- tumble blog
Also, the correct present participle is “tumblelogging”.
I recognize that it doesn’t take much skill to publish on the internet, but please make an effort to get your terminology right, even if the rest of your article is completely wrong.