Reddit mentions of Roman Republican Theatre

The answer depends on what you mean by 'Comedy', and what era you are talking about. Plautus and Terence are the only comic poets to survive in complete manuscript form (though much of Plautus is in fact not complete at all), but at least for Plautus, what we have is only a fraction of what was commonly attributed to him. Varro himself supposedly selected the "canonical" set of plays out of 100 or more attributed to Plautus, but there is very little evidence to suggest that Plautus was, in fact, a real person. (Cf. that his actual name, "Titus Maccius Plautus", is a goofy play-name, meaning something like "Floppy-dick McClown".)

Comedy as a genre was fantastically popular in the early/mid Republic, and major poets like Ennius, Naevius, and Livius Andronicus, among others, all wrote comedies, as well as other non-comic plays and poems. Within comedy, there were a number of different sub-genres: the extant plays of Plautus and Terence are part of the so-called fabula palliata, "Comedies in Greek dress", so named because they are (we think) largely adapted from other Greek plays, and so are generally set in Greece, use Greek character names, and so on. However, there were a number of other types, including comoedia togata, comedies set in Italy/Rome, and the fabula Atellana, an apparently native Italic (not Roman, but rather Oscan) comic tradition that was more physical and broad. We have lots of different fragments from these various traditions, but very few long pieces. Probably the most are from Naevius, who wrote quite a few comedies in addition to many dramas and an epic poem, as well as Caecilius Statius, a comic playwright who was perhaps a generation younger than Plautus, according to traditional dates.

As for where to find all this stuff: there are lots of different places, but few convenient ones if you don't have the original languages. One of the oldest, though by now outdated, collections is by Otto Ribbeck (Scaenicae Romanorum Poesis Fragmenta), which is available online:

http://reader.digitale-sammlungen.de/en/fs2/object/display/bsb10247541_00006.html

But, really, if you want a thorough overview of all this, then you really should check out Gesine Manuwald's Roman Republican Theater, which is very thorough, readable, well-organized, and bursting with additional bibliography:

https://www.amazon.com/Roman-Republican-Theatre-Gesine-Manuwald/dp/1107696097

Note that Manuwald's book is on Republican drama only, but there is ample evidence for interest in comedy well after this period, even into the late Imperial period. (E.g., Tertullian at one point complains about his parishioners learning bawdy songs at the theater, but not hymns.) Unfortunately, much of this material has disappeared, for whatever reason, and we have mostly indirect evidence for it in the form of e.g. commemorative inscriptions, references in contemporary authors, possible citations in authors like Petronius, and so on.