After unsuccessful googling for how to resolve the issue of WordPress asking for FTP credentials on local installations, I finally arrived at a set of working permissions for MAMP Pro in OSX. Screenshots below are from MAMP Pro v126.96.36.199 on Yosemite OS X 10.10, but the process is still the same in MAMP Pro v4 and in El Capitan 10.11 and macOS Sierra 10.12.
WordPress recommends CHMOD / file permissions of 755 for directories and 644 for files, but what I didn’t know of the top of my head was how that correlates to MAMP’s settings. I figured that out, but WordPress still wasn’t updating correctly. Then, I found this WordPress support thread where people said electronicink’s solution worked for them. Yosemite File Sharing Permissions no longer gives an FTP sharing option. Back to the drawing board! The missing key was who the Owner and Group should be. www! Duh. I’d likely changed it to myself and admin in my failed attempts at manually granting access through Finder’s Get Info feature.
Anyway, here’s the combination that finally worked for me. This dialog is accessed in the Hosts tab of MAMP PRO by clicking the people icon next to the folder icon where you choose “Document root.”