To use the alt keys to access the accented letters
In Tom Gewecke’s blog “Multilingual Mac” he mentioned that he has made available a file for this purpose.
Another source is jakwings.github.io/mac-keyboard-Esperanto/.
International keyboard with dead keys
If your main language is English, but you want to be able to type in Esperanto and other languages based on Roman letters, you can enable the layout U.S. Extended. No download is required for this method. Go to: System Preferences (Sistemaj preferoj), Language & Text (Lingvo kaj teksto), Input Sources (Enigaj fontoj), tick U.S. Extended, close. Other layouts may also be used, e.g. Finnish Extended, for Finnish and Swedish with Esperanto.
To type the accented letters, hold down the alt/option key and press the accent key (6 or B) and then the key for the letter. For instance, for Ĝ: option 6 then shift G. For ŭ: option B (for breve) then U. You can type macrons for Māori words this way too. For ō: option A then O.
U.S.ExtEsp keyboard layout uses semicolon as dead key
This method is similar to that of the International keyboard. The advantages of the U.S. ExtEsp layout are that the semicolon key is easily accessible (at least on a US keyboard), and this arrangement does not interfere with typing in English or other languages based on the Latin alphabet. Detailed information is available in ReadMe.pdf on our Downloads page.
To set up this arrangement on your Macintosh requires an OS-X virtual keyboard file. It can be downloaded from the web-site of Amerika Asocio de Instruistoj de Esperanto (AAIE) by clicking on this link:
Unzip the downloaded file and follow the instructions in the file ReadMe.pdf.
Insert menu in applications
Various programs for Macintosh have menus for inserting special characters, e.g. TextEdit, OpenOffice and LibreOffice.
Facilities exist for setting up a compose key in MacOS. Refer to Wikipedia for details.