  Efficient generation, guiding, and detection of phonons, or mechanical
vibrations, are of interest in various fields including radio frequency
communication, sensing, and quantum information. Diamond is an important
platform for phononics because of the presence of strain-sensitive spin qubits,
and its high Young's modulus which allows for low-loss gigahertz devices. We
demonstrate a diamond phononic waveguide platform for generating, guiding, and
detecting gigahertz-frequency surface acoustic wave (SAW) phonons. We generate
SAWs using interdigital transducers integrated on AlN/diamond and observe SAW
transmission at 4-5 GHz through both ridge and suspended waveguides, with
wavelength-scale cross sections (~1 {\mu}m2) to maximize spin-phonon
interaction. This work is a crucial step for developing acoustic components for
quantum phononic circuits with strain-sensitive color centers in diamond.
