There have been a few justices in the past that have "gone off their rockers" in the last few years of their careers, but from what I understand, unless they retire, they couldn't be replaced. But what if the Justice was in, say, a coma, and was therefore physically unable to work and unable to retire - is there anything that can be done to choose their successor, or would the only options be to wait for them to wake from the coma or pass away?
Federal judges and the Supreme Court justices hold their office during "good behavior". You could argue that being in a coma (or some other issue) is not "good behavior" and initiate impeachment and removal proceedings. This is untested though and may be considered a nuclear option.
If a US Supreme Court Justice is physically unable to work, are any mechanisms in place to choose their successor?
For the Chief Justice there is a rule concerning the duties of office.
Whenever the Chief Justice is unable to perform the duties of his office or the office is vacant, his powers and duties shall devolve upon the associate justice next in precedence who is able to act, until such disability is removed or another Chief Justice is appointed and duly qualified.
There is no rule concerning disability of Associate Justices.
But what if the Justice was in, say, a coma, and was therefore physically unable to work and unable to retire - is there anything that can be done to choose their successor, or would the only options be to wait for them to wake from the coma or pass away?
The latter, wait for them to wake from coma or pass away. The only way to remove a Justice is through impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors. A coma is none of these.
It should be noted that, in the case of disability, there are procedures to replace judges that are unable to continue a trial and to appoint additional judges to maintain levels in the appeals courts.