Most recently the family had their application for permanent residency knocked back by the Administrative Appeals Tribunal (AAT) on public interest grounds.
A widely criticised section of The Migration Regulations 1994 dictates that an applicant for permanent residency must be "free from a disease or condition in relation to which a person who has it would be likely to require health care or community services".
The joint letter sent to Mr Coleman from the CEOs of the Federation of Ethnic Communities Councils of Australia (FECCA) and the National Ethnic Disability Alliance (NEDA), expressed "deep concern" that the AAT decision hung on Kinley's disability.
"We are deeply concerned that Kinley’s disability status is cited as the determining factor supporting the decision to deny permanent residency to Mrs Pelden (Kinley's mother) and her family," the joint letter reads.
"We question the legitimacy of any decision where an applicant’s disability has been assessed against, or is subject to, the health requirement of the Migration Act (1958), as it is known that the health requirement unfairly discriminates against people with disability."
Last week, Greens Senator Jordon Steele-John told SBS News that the section of the act made him "physically sick".
"It is disgusting, that section of our immigration law is absolutely foul," he said.
"This thought process is based on the idea that disabled people are burdens to the Australian economy and Australian society.
"Not only is that deeply ableist, deeply discriminatory but in the era of the NDIS it is something that is totally out of line with the rest of our social service policy."
A spokesperson from the Department of Home Affairs previously told SBS News that the health requirement was "an objective assessment to determine whether the care of the individual during their stay in Australia would likely result in significant costs to the Australian community or prejudice the access of Australian citizens and permanent residents to services in short supply."
Both Kinley's family and the organisations behind the letter claim that Kinley is a "healthy young man with a disability, who has no known health issues".
"His parents are economically and financially well-positioned to meet the day-to-day expenses of this young man," the letter reads.
While living in Australia, the family claim Kinley has learnt to communicate using Australian Sign Language (AUSLAN) - a language that is not used in Bhutan.
"We hold deep concerns for the well-being and prospects of Kinley if he and his family were required to leave Australia Kinley will be forced to live in a country where he cannot communicate with those around him, as Auslan is a language group only signed by the Australian deaf community," it continued.
"He will be left voiceless and isolated in a country that is not home."
On Thursday, rallies calling for a halt to the deportation are planned to take place outside the Department of Home Affairs offices in Sydney and Melbourne.
The Minister of Immigration is unable to comment on individual cases.