There are 2 treatments that can treat both issues.
Picosecond lasers: They are able to reduce/remove pigmentation which occurs in both dark eye circles and pigmentation. My personal favourite is Picosure which has more than 20 clinical studies proving its efficacy, US FDA-approved and has reproducible results for the 2 Issues consistently.
Teoxane Redensity 1 beauty booster + Redensity 2 dark eye circle filler can also treat both issues. Both have the Dermal Restructuring Complex (DRC) with 8 amino acids, 3 Anti-oxidants (including glutathione), 2 minerals and 1 vitamin, which lightens dark circles and pigmentation.
If your overall skin condition is considered severe, I would recommend a combination of treatments so as to treat it effectively in a shorter period of time.