if they are opposed to the idea of euthanasia and you live in one of the 99% of countries that allow it, then there is very little that you can do.
usually people seek the help of a lawyer to put in their testament that they want to die in a dignified way if they are unable to comunicate it either because they end up paralized or in a coma, but it is kinda suspicios, specially if your family already knows that you are suicidal.
there is also a Do not resucitate order, which is basically a document that specifies that paramedics can't perform cardiopulmonar resuscitation on you, but most of them just ignore it even if you have it tattoed in your chest.
the best you can do is communicate it to them directly and explain that if you are ever in such situation, you just whish to be put down. of course you shouldn't mention anything suicide related, that way they will know your wishes.