The selection of a suitable model hinges on various considerations, including the accessibility of input data, the required spatial and temporal precision, the specific hydrological phenomena under scrutiny, and your proficiency with the model. Generally speaking, when estimating runoff in regions exceeding 200 km², a distributed hydrological model typically proves more suitable than empirical or lumped models.
But if you specifically looking for a manual method: Unit hydrograph methods, such as the Snyder's or the SCS Unit Hydrograph methods, can be used to estimate runoff hydrographs from rainfall data.
The Budyko framework can yield a rough first-order estimate of runoff, with very little effort. You will need areal precipitation estimates, as well as estimates of potential ET (which can be made using met data).
Such an estimation techique is especially useful if there a nearby watershed or watersheds (with similar climate & topography) where runoff data is available (the accuracy of the Budyko method for runoff estimation can then be checked for these nearby watershed(s)).
I will make the case for putting aside your model and going to the field and developing a stage to discharge relationship for a watershed this large. A rating relationship with as few as four or five points will provide better information than rough modeling efforts. Install a logging rain gage at the same time and get that data on site, too. I realize you may not have the time or money to develop such a relationship, however, so you might be forced to model things. Good luck!