This paper presents a design and operating principle of a fluid viscosity sensor with an amplitude output based on a differential piezoelectric transformer. Sensors with one-, two-, and three-degree-of-freedom oscillation systems are investigated, and sensors design based on coupled oscillations of composite piezoelectric transformers is proposed. Simulation techniques with simplified electrical circuit equivalents of oscillation systems of primary transducers are utilized for studying metrological characteristics of the sensors. It is shown that rational use of coupled modes in primary transducers improves the metrological characteristics of the sensors and enhances their functionality. Coefficients of relative sensitivity and measurement efficiency provide the basis for evaluation of optimal design of sensors. There is a variety of optimal designs for transducers based on coupled oscillations that result in enhanced functionality, high sensitivity, and measurement efficiency.