You can say tanner, it's the comparative form of the adjective tan.
Adjectives have three forms: positive, comparative, and superlative.
The simplest form of the adjective is its positive form. When two objects or persons are being compared, the comparative form of the adjective is used. When three or more things are being compared, we use the adjective’s superlative form.
The comparative forms of most adjectives, however, are formed by adding the suffixes –er and –est, or by placing the words more and most in front of the positive form.
Few adjectives, like good and bad form their comparatives with different words.
See the rules for forming comparative adjectives at DailyWritingTips.
Check out 9 Clever Self-Tanning Tips You've Never Heard featured at the Huffington Post.
Learn what causes a sunburn and suntan at the American Academy of Dermatology and find out the dangers of tanning at The Skin Cancer Foundation.