Do you play yourself, and if so what is the level of your knowledge and skill? (I'm speculating you might, otherwise why have a piano?)
If you do play, and have some knowledge of music, then I think it is perfectly feasible to start beginners off yourself. There are many tutor books, often with a CD illustrating what the music should sound like, for an outlay probably less than the cost of one hour with a private teacher. Also, there are on-line demonstrations of piano for young children, and adults, though some are possibly not all that good.
I ran a keyboard club with Yr6 children, did recorder groups for ten years, and also coached children to play percussion to accompany the Christmas production each year. There seems to be an aura of mystery surrounding learning an instrument, as if it were beyond the capabilities of mere mortals!
Certainly, to get to the higher Grades, and a knowledge of Theory, does require study, practise, and dedication over a number of years. But to introduce students to the first rungs of the musical ladder - whether children or adult - to start to experience the pleasures of making music, could be within the grasp of many people.
Precision and accuracy are important aspects, and just because early pieces might be easy, they should still be played with as much feeling and sensitivity as later difficult pieces. Also listening to as wide a range of piano and other music, thinking constructively about the piece, its rhythm, speed, phrasing and overall 'feeling' of the music, is useful.
Is your piano acoustic (and in reasonable condition and in tune) or an electronic instrument? It doesn't really matter which, but good condition is necessary to make it easier for the beginner.