The Collaborative International Dictionary of English v.0.48:

Teeter \Tee"ter\, v. i. & t. [imp. & p. p. Teetered; p. pr. &
   vb. n. Teetering.] [Prov. E. titter to tremble, to seesaw;
   cf. Icel. titra to tremble, OHG. zittar[=o]n, G. zittern.]
   To move up and down on the ends of a balanced plank, or the
   like, as children do for sport; to seesaw; to titter; to
   titter-totter. [U. S.]
   [1913 Webster]

         [The bobolink] alit upon the flower, and teetered up
         and down.                                --H. W.
                                                  Beecher.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

42 Moby Thesaurus words for "teetering":
   Lissajous figure, alternation, back-and-forth, coming and going,
   dilapidated, doddering, ebb and flow, fluctuation, flux and reflux,
   groggy, oscillation, pendulation, ramshackle, reciprocation,
   rhythmic play, ricketish, rickety, rocky, seesaw, seesawing, shaky,
   shifting, shuffling, sine wave, spidery, spindly, teeter,
   teeter-totter, teeter-tottering, teetery, to-and-fro, tottering,
   tottery, tumbledown, unsteady, ups and downs, vacillation,
   variation, vicissitude, wavering, wigwag, wobbly