In Icelandic we have the neopronoun "hán", which I know some nonbinary folk here use regularly. I'm not a native speaker so I can't properly evaluate how awkward it is, and I've definitely seen grumbling from natives about how it doesn't feel natural, but to me as a learner it feels completely reasonable and fits into the rather complicated grammar of Icelandic perfectly.
Just like how English distinguishes between subject/object/possessive for pronouns (I/me/my, he/him/his, she/her/her, they/them/their), Icelandic has 4 cases for nouns and pronouns. Hán behaves exactly like a regular neuter noun when inflected, declining like "hán/hán/háni/háns" for each of Icelandic cases. Compare the regular neuter word borð (table), which declines like "borð/borð/borði/borðs".
Adjectives also decline for gender in Icelandic, but as you may have guessed nonbinary folk predominantly use the neuter gender, which agrees with the pronoun hán. There of course already existing a third person neuter pronoun in Icelandic, "það", but its meaning is more like the English "it" and most people prefer understandably to not to go by it.
Also interesting but not pronouns is how Icelanders use names. Basically Icelanders don't have a family name the way most other western countries do (... with exceptions), their last name is instead the name of their father, in possessive, plus -son or -dóttir. So if you are the son of your father, Einar, your last name would be Einarsson, literally "Einar's son". If you were the daughter of Einar, your last name would be Einarsdóttir, literally "Einar's daughter". This system of surnames is called patronymic surnames, and recently there has been more matronymic surnames as well -- for example former football player Heiðar Helguson's mother would have been called Helga, and his last name means "Helga's son".
This is of course problematic for nonbinary people who do not wish to use either -son or -dóttir, but recently it was allowed to use the neuter ending -bur instead, which repurposes an archaic word meaning "son" but is just used to mean a gender neutral "child" nowadays.
In Icelandic we have the neopronoun "hán", which I know some nonbinary folk here use regularly. I'm not a native speaker so I can't properly evaluate how awkward it is, and I've definitely seen grumbling from natives about how it doesn't feel natural, but to me as a learner it feels completely reasonable and fits into the rather complicated grammar of Icelandic perfectly.
Just like how English distinguishes between subject/object/possessive for pronouns (I/me/my, he/him/his, she/her/her, they/them/their), Icelandic has 4 cases for nouns and pronouns. Hán behaves exactly like a regular neuter noun when inflected, declining like "hán/hán/háni/háns" for each of Icelandic cases. Compare the regular neuter word borð (table), which declines like "borð/borð/borði/borðs".
Adjectives also decline for gender in Icelandic, but as you may have guessed nonbinary folk predominantly use the neuter gender, which agrees with the pronoun hán. There of course already existing a third person neuter pronoun in Icelandic, "það", but its meaning is more like the English "it" and most people prefer understandably to not to go by it.
Also interesting but not pronouns is how Icelanders use names. Basically Icelanders don't have a family name the way most other western countries do (... with exceptions), their last name is instead the name of their father, in possessive, plus -son or -dóttir. So if you are the son of your father, Einar, your last name would be Einarsson, literally "Einar's son". If you were the daughter of Einar, your last name would be Einarsdóttir, literally "Einar's daughter". This system of surnames is called patronymic surnames, and recently there has been more matronymic surnames as well -- for example former football player Heiðar Helguson's mother would have been called Helga, and his last name means "Helga's son".
This is of course problematic for nonbinary people who do not wish to use either -son or -dóttir, but recently it was allowed to use the neuter ending -bur instead, which repurposes an archaic word meaning "son" but is just used to mean a gender neutral "child" nowadays.