A website which specialises in Scottish Blogs lists only three for the Borders:
gemmak's BLOGS : infoThe day to day ramblings of a computer addicted woman and her cats who escaped the 'big city' for an idyllic life in the middle of nowhere.
Martin Frost : infoA very grumpy old man
Musings from the Merse : infoA daily rant from the Scottish Borders which has had some notoriety in the Scottish press Modesty prevents me from indicating my favourite.