No color is 'rare', but some are harder to find. Specifically BSE Yellows, BSE/Chocolate Oranges and 'Pinks' (Orange with heavy irid). Stable Butterflies are perhaps the hardest to find. Purple and Green don't exist in Betta, and technically Pink doesn't either. Some people claim they have them, but it's usually a combo of a red fish with blue wash and correct lighting or Turquoise, respectively. People like to photoshop pistures to make fish look colors that don't exist. I'll go find some pics for you.
Pic 1 - Chocolate Orange HMRT - These exist, but are hard to find.
Pic 2 - BSE Orange HMPK - 'BSE' refers to pineapple-like scales (black tips) and specifically Orange are really hard to find... This is the only pic off the internet that I could find, and I'm pretty sure he would be classified as a Chocolate, too.
Pic 3 - Yellow BSE - Unsure of the tail type on this girl, I think she's just a PK. One of the only pics of a BSE Yellow on the internet.
Pic 4 - 'Purple' (Copper) HM - Beautiful boy, but his irid is what makes him look purple. He's actually a Copper of some type.
Pic 5 - ? - A great example of a Photoshopped purple.
Pic 6 - 'True Pink' Dalmatian HM - This is as close to pink as you can get; Orange with extreme Irid under the right lighting.
Pic 7 - ? - Photoshopped 'Pink' HMPK.