Here are a few solutions you can found while searching the Internet :

• Disabling binary logs via the mysql config file
• Deleting iblogfileXXX files
• Deleting mysql-bin.~ files
• Uninstalling and re-installing MAMP
• etc…

None of them will work. Most of the tips are for MAMP version older than 4.1.
Starting version 4.2.0 using the following solution found on a Japanese woman evangelist blog worked for me !

What you have to do is stopping MAMP and edit the mysql config file located here :

C:\MAMP\conf\mysql\my.ini

Just after the innodb related settings and before the mysqldump, for example :

#innodb_flush_log_at_trx_commit = 1
#innodb_lock_wait_timeout = 50

[mysqldump]
quick
max_allowed_packet = 16M

Add the following line :

innodb_flush_method = normal

Which results in :

#innodb_flush_log_at_trx_commit = 1
#innodb_lock_wait_timeout = 50
innodb_flush_method = normal

[mysqldump]
quick
max_allowed_packet = 16M

Restart MAMP and now it should work perfectly ! ! !

Feel free to get in touch with me in the comments to tell me if it works for you.