Discussions about how to write Gutnish has been alive since the days of the Säve brothers in the 19th century. They made great efforts to collect the language as it was spoken around the country and in the villages.
Both were gutnish and Carl Säve, the younger brother born in 1812, would later become the first professor in Sweden in scandinavian languages. He of course specialised in Gutnish.
In the 1970´s the first concrete suggestion to a gutnish orthography was presented by Gertmar Arvidsson from Sproge in Gotland. This orthography did not gain any ground and seems not to have been used since then.
In the late 80´s the gutnish cultural profile and musician Bert Alvengren from Habdum in Gotland initiated the best and most suitable orthography this far for the gutnish language. This orthography was used and supported by an association promoting gutnish culture and language called Propago.
After a decade or so this association rewrote it all and started afresh with an entirely new spelling system that began with an adjusted alphabet, where several letters were changed and adapted to the language itself.
After another decade the members more or less split and started to work on their own. I am one of them.
In 2006 another association (called Gutamålsgillet in Swedish) promoting the gutnish language came out with some recommendations for the spelling of the gotlandic language. Though it wasn´t an orthography per se, it had rules for spelling even if the rules were quite loose.
In 2011 Bert Alvengren as mentioned before published a new orthography that was used in a book called ´ABC-bok på gutniska´ (a swedish title). This orthography is based on the last work and orthography that Propago worked with, but still radically rewritten.
In 2012 another linguistic association called Malsaudin presented its spelling system on www.malsaudin.com. It is a project I to a lesser part have been supporting since it is basically based on the Propago norm that too. I use this orthography even if I too have used another one before.