I need to make a companion perk for my companion mod. The idea I had is too increase Charisma by 1, Speech by 10, and have the player suffer no negative karma losses.

How would I go about doing this, specifically the last part? What scripts would I need to write? Please help!

Charisma and Speech can be handled by a simple ability. As for the no karma loss, I can't write the script from the top of my head, but I'd create a global that is set to the player's current karma when the follower is hired, and then in the script I'd check if the player has the new companion's perk, and if yes then check if the player's karma is lower than the global, and if yes then set player's karma to the value of the global. Or if you can't set the value directly I'd make it calculate the difference between the current value and the global and then reward the palyer with that amount of karma. However, this would still display the message that you lost and gained karma.

This link might prove useful to you: http://geck.gamesas.com/index.php?title=Scripting_for_Beginners

Karma is an actor value, so you can check it's value with

player.GetActorValue karma

It's special though and you can't set it directly like most actor values. You will need to use http://geck.gamesas.com/index.php?title=RewardKarma instead.