We report our findings on a new quasi-periodic oscillation (QPO) and a long period from the ultraluminous X-ray source (ULX) X-2 in nearby galaxy NGC 4736 based on the Chandra and XMM-Newton archival data. To examine the timing properties, power density spectra of the source have been obtained using Fast Fourier Transform. Also the spectral parameters of the source have been calculated by obtaining and fitting the energy spectra. Power density spectrum of this source reveals a QPO peak at with an fractional rms variability of 16 % using the Chandra data (in the year 2000-lower state of the source). The XMM-Newton data analysis indicates a peak at with a fractional rms variation of 5 % (in the year 2006-higher state of the source). These recovered QPOs overlap within errors and may be the same oscillation. In addition, we detect a long periodicity or a QPO in the Chandra data of about (5.2 +/- 2.0)x10(-5) Hz (similar to 5.4 h) over 3 sigma confidence level. If this is a QPO, it is the lowest QPO detected from a ULX. The mass of the compact object in ULX X-2 is estimated using the Eddington luminosity and a disk blackbody model in the range (10-80) M-circle dot.