Word for making an implication with tone

Solution 1:

Consider intonation.

Definition: the ​sound ​changes ​produced by the ​rise and ​fall of the ​voice when ​speaking, ​especially when this has an ​effect on the ​meaning of what is said; The use of changing pitch to convey syntactic information.

Example: Even if your friend claims she's not upset by the death of her pet iguana, her intonation may tell a different story.

Solution 2:

Although intonation may seem an obvious answer to the OP -

manner of utterance of the tones of the voice in speaking; modulation of the voice; accent (OED)

OED examples of its usage in this respect make clear that more often than not intonation actually refers, narrowly, to its musical sense -

The utterance or production (by the voice, or an instrument, etc.) of musical tones: in reference to manner or style, esp. to exactitude of pitch or relation to the key or harmony. (OED)

While it is true that the OP does specifically refer to 'tone', the examples given achieve their alternative meanings by virtue of variations not only in 'tone', but also 'rhythm' and 'cadence'. For these reasons it seems to me that a better word to answer the OP is prosody, which includes intonation, but also these other elements -

a suprasegmental phonological feature such as intonation and stress. Also: such features collectively; the patterns of stress and intonation in a language.(OED)