Plate tectonics on earth are unique in our solar system and, as far as we can tell, in the galaxy, because of our oceans. Tectonic activity could occur on many different planet types, but Earth-like plates are being cycled down into the mantle nearly continuously. A combination of rheological and geophysical observations suggest that the physical properties of the oceanic asthenosphere are strongly influence by the presence of small amounts of dissolved water. In essence, the oceans hydrate and lubricate the plates for subduction, and also make them pliable. The edges of plates are marked by dry areas: the oceanic plates may be defined by a dehydration boundary that is formed as a result of melting at oceanic spreading centers. Where there is no water, the dehydrated asthenospheric crust forms the edge of an oceanic plate. Subduction is important for re-introducing water into the mantle. How do we know water is going into the mantle? Olivine in a mantle residue of a basaltic melt—the kind found in a volcanic arc—has about the same 6%wt water as what we estimate for the oceanic asthenosphere.
Thus it is possible that even if a subduction like process occurred on your planet, the rheological properties of a dry upper mantle would inhibit the formation of Earth-like plates.
It is unlikely that your planet would have terrestrial plate tectonics without a lubricating and hydrating ocean. And, while you may lubricate with an ocean of another liquid, you need to be introducing hydrogen into the asthenosphere if you are going to have a habitable planet.
I can not help with what other liquid would serve this purpose, sorry.