Why were pulsars not discovered in the visual spectrum?

I'm going to raise some of the same points the other answers have, but in slightly more detail.

There are two main types of visible light coming from a pulsar: thermal black body emission from the surface of the neutron star, and optical synchrotron radiation originating in the magnetosphere. The first problem with observing either of these lies in the fact that neither contributes significantly strong emission. The Crab pulsar appeared as a magnitude $+17.7$ V-band source in the initial optical observations (see Cocke et al. 1969), pushing the limits of what could be observed at the time.

The vast majority of neutron stars do not display substantial thermal emission ($\lesssim1\%$ of total optical radiation), meaning that optical synchrotron radiation is a much better thing to look for at visible wavelengths. However, given the dimness of the source, you need to understand the radio/x-ray pulsations of the neutron star. The confirmation of the first optical detection involved a complicated setup to synchronize with the target and time-average the signal (Nather et al. 1969), and this would not have been possible had the Crab not already been detected at radio wavelengths. The technology existed, but one wouldn't casually scan the sky at optical wavelengths with it; that would be fairly pointless unless you had a pulsating target.

To expand on a point made in Thomas's answer, systems for detecting optical pulsars don't naively use CCDs, but instead use a principle called photon counting, which, well, counts photons.

Astrophotography of distant objects traditionally was done by exposing photographic plates for a few minutes or even hours, and then developing them. With this procedure it is simply not possible to detect the intensity variations of pulsars (varying in the seconds or even milliseconds range).

I doubt if this is even possible now, by using CCD sensors instead of photographic plates.

Optical pulsars aren't very bright, and we've only found 6 of them so far.

Wikipedia says:

There are very few of these known: the Crab pulsar was detected by stroboscopic techniques in 1969, shortly after its discovery in radio waves, at the Steward Observatory. The Vela pulsar was detected in 1977 at the Anglo-Australian Observatory, and was the faintest star ever imaged at that time.

As Thomas mentions, the long exposures typically used to capture images of faint objects cannot detect the pulsing of a pulsar, unless you use stroboscopic techniques. And you're not likely to try using a stroboscopic image capture unless you suspect that the object may be pulsing.

However, from the Wikipedia article on the Crab Pulsar:

Jocelyn Bell Burnell, who co-discovered the first pulsar PSR B1919+21 in 1967, relates that in the late 1950s a woman viewed the Crab Nebula source at the University of Chicago's telescope, then open to the public, and noted that it appeared to be flashing. The astronomer she spoke to, Elliot Moore, disregarded the effect as scintillation, despite the woman's protestation that as a qualified pilot she understood scintillation and this was something else. Bell Burnell notes that the 30 Hz frequency of the Crab Nebula optical pulsar is difficult for many people to see.