Try this:
[This is a three part process]
Part One: [Fully Uninstall TechnicLauncher]
Click on Finder to open a Finder window.
Click on "Go" in your menubar, then "Go To Folder".
Type in "~/Library/Application Support" without the quotation marks.
Delete the folder "techniclauncher".
Delete the Techniclauncher application.
Part Two: [Downgrade to Apple's Java 6 instead of Oracle's Java 7]
Go here and wait for the page to load.
You should get something like this if you have Oracle's Java 7 installed.
Once you verify that you have Oracle's Java 7 installed, click on Finder to open a new Finder window.
In the search bar search "JavaAppletPlugin.plugin". [Note: Make sure that you select "This Mac"]
Delete/Move "JavaAppletPlugin.plugin" to your trash. [Note: You will only be able to empty trash when your web browser, minecraft, techniclauncher, any application that uses java is closed]
Go to your applications, go into the "Utilities" folder, and open Terminal.
Paste this into the Terminal window and press [ENTER]. [Note: You will have to type in your password. Your password will not show up while typing, but it IS being inputted]
Type "logout" into the Terminal window.
Close and quit Terminal.
Go here and wait for the page to load.
Make sure that you no longer have Oracle's Java 7 installed anymore.
Part Three: [Reinstall TechnicLauncher]
Go here and download the latest Techniclauncher application for Mac OS X
Open Techniclauncher after downloaded, and download all files needed for Technic/Tekkit/YogBox/HackMine/etc. to run by selecting the respective mod and typing in your credentials and clicking login.
Technic/Tekkit/YogBox/HackMine/etc. should be working now.