Emotion-driven melody harmonization aims to generate diverse harmonies for a single melody to convey desired emotions. Previous research found it hard to alter the perceived emotional valence of lead sheets only by harmonizing the same melody with different chords, which may be attributed to the constraints imposed by the melody itself and the limitation of existing music representation. In this paper, we propose a novel functional representation for symbolic music. This new method takes musical keys into account, recognizing their significant role in shaping music's emotional character through major-minor tonality. It also allows for melodic variation with respect to keys and addresses the problem of data scarcity for better emotion modeling. A Transformer is employed to harmonize key-adaptable melodies, allowing for keys determined in rule-based or model-based manner. Experimental results confirm the effectiveness of our new representation in generating key-aware harmonies, with objective and subjective evaluations affirming the potential of our approach to convey specific valence for versatile melody.