How to change [option + key] international shortcut in OS X
Stumbled upon this post when trying to achieve the same mapping with Karabiner-Elements. 
The old "Karabiner" does not work with Sierra and above and have been replaced with Karabiner-Elements. 

I managed to achieve the behaviour desired by original poster in Karabinier-Elements by adding the configuration below to karabinier.conf so I posted this as reference for others that stumble in here for same reason. 

It is based on the "standard" way to enter umlaut characters with a US keyboard, e.g.
option+u, a => ä
option+u, o => ö
and
option+a => å

(in section "complex_modification" -&gt; "rules")
"rules": [
       {"description": "left_option ['; to åäö",
        "manipulators": [
            {"type": "basic",
            "from": {
                "key_code": "open_bracket",
                "modifiers": { "mandatory": [ "left_option" ] }
            },
            "to": [
                {"key_code": "a",
                 "modifiers" : [ "left_option" ]
                }]
            },
            {
            "type": "basic",
            "from": {
                "key_code": "open_bracket",
                "modifiers": {
                "mandatory": [
                    "left_option",
                    "left_shift"
                ]
                }
            },
            "to": [
                {"key_code": "a",
                 "modifiers" : [
                 "left_option",
                 "left_shift"
                 ]

                }
            ]
            },

            {
            "type": "basic",
            "from": {
                "key_code": "quote",
                "modifiers": {
                "mandatory": [
                    "left_option"
                ]
                }
            },
            "to": [
                {"key_code": "u",
                 "modifiers" : [
                 "left_option"
                 ]
                },
                {"key_code": "a"}
            ]
            },
            {
            "type": "basic",
            "from": {
                "key_code": "quote",
                "modifiers": {
                "mandatory": [
                    "left_option",
                    "left_shift"
                ]
                }
            },
            "to": [
                {"key_code": "u",
                 "modifiers" : [
                 "left_option"
                 ]
                },
                {"key_code": "a",
                 "modifiers" : [ "left_shift" ]}
            ]
            },

            {
            "type": "basic",
            "from": {
                "key_code": "semicolon",
                "modifiers": {
                "mandatory": [
                    "left_option"
                ]
                }
            },
            "to": [
                {"key_code": "u",
                 "modifiers" : [
                 "left_option"
                 ]
                },
                {"key_code": "o"}
            ]
            },

            {
            "type": "basic",
            "from": {
                "key_code": "semicolon",
                "modifiers": {
                "mandatory": [
                    "left_option",
                    "left_shift"
                ]
                }
            },
            "to": [
                {"key_code": "u",
                 "modifiers" : [
                 "left_option"
                 ]
                },
                {"key_code": "o",
                 "modifiers" : [ "left_shift" ]}
            ]
            }
        ]
        }] // end "rules"