Definitions of singsong:

• noun:   a regular and monotonous rising and falling intonation
• noun:   informal group singing of popular songs
• verb:   move as if accompanied by a singsong

  Example: "The porters singsonged the travellers' luggage up the mountain"

• verb:   speak, chant, or declaim in a singsong
• adjective:   uttered in a monotonous cadence or rhythm as in chanting

  Example: "A singsong manner of speaking"