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We present results of targeted searches for signatures of non-radialoscillation modes (such as r- and g-modes) in neutron stars using {\it RXTE}data from several accreting millisecond X-ray pulsars (AMXPs). We search forpotentially coherent signals in the neutron star rest frame by first removingthe phase delays associated with the star's binary motion and computing FFTpower spectra of continuous light curves with up to $2^{30}$ time bins. Wesearch a range of frequencies in which both r- and g-modes are theoreticallyexpected to reside. Using data from the discovery outburst of the 435 Hz pulsarXTE J1751$-$305 we find a single candidate, coherent oscillation with afrequency of $0.5727597 \times \nu_{spin} = 249.332609$ Hz, and a fractionalFourier amplitude of $7.46 \times 10^{-4}$. We estimate the significance ofthis feature at the $1.6 \times 10^{-3}$ level, slightly better than a$3\sigma$ detection. We argue that possible mode identifications includerotationally-modified g-modes associated with either a helium-rich surfacelayer or a density discontinuity due to electron captures on hydrogen in theaccreted ocean. Alternatively, the frequency could be identified with that ofan inertial mode or an r-mode modified by the presence of a solid crust,however, the r-mode amplitude required to account for the observed modulationamplitude would induce a large spin-down rate inconsistent with the observedpulse timing measurements. For the AMXPs XTE J1814$-$338 and NGC 6440 X-2 we donot find any candidate oscillation signals, and we place upper limits on thefractional Fourier amplitude of any coherent oscillations in our frequencysearch range of $7.8\times 10^{-4}$ and $5.6 \times 10^{-3}$, respectively. Webriefly discuss the prospects and sensitivity for similar searches with future,larger X-ray collecting area missions.

A Non-radial Oscillation Mode in an Accreting Millisecond Pulsar?