Mr Cole-Hamilton said he was “proud” of the work Liam McArthur had done on the issue.
He was speaking as consultation on Mr McArthur’s Assisted Dying Bill got under way on Thursday.
However, Lord Wallace, a former Scottish Liberal Democrat leader who is now the Moderator of the General Assembly, highlighted the Church of Scotland’s opposition to the proposals.
Mr McArthur’s Bill seeks to legalise assisted dying as a choice for adults who are both terminally ill and mentally competent.
Mr Cole-Hamilton said: “I am proud of my colleague Liam McArthur, who launches the consultation on his Bill to introduce assisted dying today.
I want the choice, if I’m in agony and beyond the reach of palliative care, to say ‘this far and no further’.
“Everyone should have the right to a good death.”
Holyrood has twice voted down attempts to introduce similar legislation, but Mr McArthur insisted there were “strong safeguards” in his proposals – which are supported by Dignity in Dying Scotland, Friends at the End and the Humanist Society Scotland.
Two doctors would have to independently confirm a person is terminally ill before assisted suicide can be considered, as well as establishing they have the mental capacity to make such a request and have not been coerced into it.
Doctors would also need to ensure the person has been fully informed of options for palliative and hospice care.
The person making the request would have to sign a written declaration, which would be followed by a “period of reflection”.
They would then have to be able to administer the life ending medication by themselves, with the plans making clear it will continue to be a criminal offence to end someone else’s life directly.
All assisted deaths would also be recorded and reported for safety, monitoring and research purposes.
But Lord Wallace made clear: “The General Assembly has consistently and repeatedly expressed support for the status quo with regards to the law which prohibits assisted dying in all its forms.
“The current societal protection of life is clear and to move away from this would involve more than a simple modification of the law and would represent a ‘crossing of the Rubicon’ from which there would be no return.
“This would have profound effects on how society regards those in our communities who are vulnerable, not just the elderly and infirm, but also those with disabilities and those who are unable to speak up to protect themselves.”
The group Care Not Killing, which includes the Catholic Church and the Muslim Council of Scotland, has said it expects thousands of Scots to sign a petition it has launched against the legislation.
But speaking at the start of the consultation, which runs until December 22, Mr McArthur said: “In my time as an MSP I have heard from many dying people and grieving families who have been failed by the current blanket ban on assisted dying.
“I have watched other countries, such as Australia and New Zealand, put new laws in place to ensure their citizens can have a peaceful and dignified death and I believe that the time is right for Scotland.”