"yr" as an all-purpose contraction for your
has been around at least since the 50s
, when Jack Kerouac
(everyone's favorite drunken misogynistic crystalline delicious bloated genius) published his Essentials of Spontaneous Prose
In 1959, Kerouac wrote a letter to Allen Ginsberg detailing his Belief and Technique for Modern Prose, a list of essential rules for creating exuberant roaring text. The first item in the list reads, "Scribbled secret notebooks, and wild typewritten pages, for yr own joy." Kerouac didn't care much for traditional spelling and grammar, and why should he, when this simple 2-letter word is hard to mistake. The use of "yr" in Beat (and faux-Beat) poetry and prose does get tediously precious - but it's also a graceful detour around the ugly textual snag of using "your" when "you're" is called for.
"yr" may well have been around before the Beat poets. Please add on, if you've more information - I asked Google; it's not the easiest search to define. But, um, I can prove with my eyes shut that the earliest appearance of this term is not courtesy of yr silly old Sonic Youth.