First of all, add or replace? Replacing the player portraits are pretty easy, there's 4 or 5 files and you just take your pictures and do some photoshoping to get replace them over the existing ones. Adding new ones requires editting some other files that tell the game how the UI is set up and where to find the pictures but its still doable.

Gimp: with the DDS plug-in (DDS files are mainly for ship textures). 

Look at ZombiesRus' guide UI - Research Button which is almost exact same steps

Make a mod with a Textures folder (MyMod\Textures)

inside you will need...

Player_Portrait_Button.tga
Player_Portrait_Large.dds   needs plugin
Player_Portrait_Medium.tga 
Player_Portrait_Small.tga
Player_Portrait_Window.tga

I got these from 
C:\Program Files (x86)\Stardock Games\Sins of a Solar Empire - Trinity\Diplomacy\Textures 

Start with the large and shrink the image to fit the other sheets

Post back if you want to continue.