While I've never heard of a general Niger-Congo religion, people do often talk about Bantu mythology. This makes sense, as much of the Bantu Expansion was probably more recent than the Indo-European one.

On the Asian side, you'll here people discuss common elements of Polynesian mythology or Melanesian mythology (and I assume also Micronesian mythology), but in terms of mainland Asia--besides the sub-continent--I'm not sure I've heard of any large scale proto-mythology (except for studies into pre-Buddhist Chinese mythology). Elsewhere in Asia, the closest you get is something like "Tengrism", which is the proposed pre-Muslim/Buddhist/Christian Mongolian and Turkic religion (unfortunately, the study of it as far as I've seen is more concerned with nationalism than accurate history, so there's nothing in particular I can recommend). There's also the Circumpolar Shamanistic tradition--Alice Beck Kehoe's Shamans and Religion is a good, critical starting place (if I'm remembering correctly), as again a lot of the scholarship is imaginative garbage.

Proto-Cushitic.

The Proto-Cushitic peoples were nomadic and pastoral, worshipped a henothistic clan-based pagan religion that involved fertility cults, animal sacrifice, clan founder veneration (with Cushitic clan founders being made into Godlike/Godly figures), and in a belief of angelic-like beings called 'Ayaanle' (in Somali) or 'Ayanna' in Oromo, with different Cushitic languages having different variations of the word. Also, demons and demonic influence was an important part of Cushitic paganism, at war with the angelic and good 'Ayaanle' who served as intermediates between the Cushitic clans and clan priests and the Supreme Cushitic diety 'Waaq' and the pantheon of lower clan-affliated Cushitic gods.

Genetic continuity from the ancestral Cushitic group that spoke Proto-Cushitic is largely intact, and is best preserved amongst the Somali and Afar ethnic groups, as these two groups have the highest levels of the 'Ethio-Somali' genetic component that is identified as a ancestral genetic component of the proto-Afroasiatic speakers, representing the majority of their ancestry. Some Cushitic groups have experienced heavy genetic mixture with incoming Semitic groups, most notably the highlander Orthodox Agew and Muslim Beja clans, or with Nilo-Saharan groups, most notably the Dassanech, El-Molo, and Oromo. However, the genetic base for the Horn of Africa is still, by far, a genetic continuity of the ancestral proto-Cushitic.

Unlike PIE, the Cushitic languages were not spread by elite groups of warriors, or by displacing existing langauges. Rather, since proto-Cushitic predates proto-Indo-European by thousands of years to a time period when the Horn of Africa and most of the world was made up of hunter-gatherer bands and not established populations, the Cushitic languages and ethnic groups were actual splintering from the original proto-Cushitic group and large scale migrations of Cushitic speakers who were direct genetic descendants of the proto-Cushitic group into mostly uninhabited areas. Hence, the lack of substratum in the vast majority of Cushitic languages, with linguistic differences being the result of millinia of linguistic evolution and not a merging of populations/cultures as is typical of most Indo-European sub-familial linguistic differences. This can also be seen from the general strong genetic and physical resemblance of the Cushitic peoples, with Bejas looking no different from the Somali or Afar physically despite thousands of years of little to no intermarriage or much contact between the Somali and Afar and their northern Beja cousins, a testimony that the Cushitic speakers have not only a cultural/linguistic heritage from the proto-Cushitic group, but the vast majority (if not all) of their genetic ancestry as well.

Another way that proto-Cushitic is similar to proto-Indo-European is the large tract of land that Cushitic/proto-Cushitic spread to. From Southern Egypt to nearly south as South Africa, as far the eastern side of the Great Lakes was the realm of the Cushitic nations. However, unlike the Indo-European langauges, the area occupied by the Cushitic peoples was mostly lost by the Bantu Migrations, with Bantu peoples assimilating and wiping out most Cushitic groups south of Kenya and the Equator and later a Nilotic expansion which assimlated and wiped out most Cushitic groups in Kenya and Tanzania. These two expansions, as well as a Semitic expansion into Ethiopia of Ethiosemitic speakers who quickly assimilated local Cushitic groups, and the later Arab invasions which assimilated and Arabized Cushitic nomadic groups into Arab Bedioun tribal groups, with the process currently ongoing (the Beja are currently undergoing heavy Arabization, which they have for nearly 1000 years) has left Cushitic speakers confined to the Horn of Africa. As such, stories abound amongst the Cushitic peoples of the Horn of Africa of 'lost cousins' who happened to survive as a distinct group and the legacy of so much Cushitic nations being non-existent and wiped away from history and how these 'lost peoples' serve as grim reminders to not miscegenate with people who 'are not us'. This is in contrast to the rapid spread of Indo-European languages in the last 500 years.

Also, the construction of Cairns and Stalae by Cushitic peoples as pagan religious monumental structures is an expression of the common pagan faith the Cushitic peoples adhered to. This pagan faith was later synchronized with early Christianity, Islam, and Judaism to form the pagan-Hebraic religion of the Agews of antiquity, the syncretic Islam of the Somali clans, and the Ethiopian Orthodox Christian faith of the Ethiosemitic highlanders. A common element in the syncretic Cushitic paganism-Abrahamic monotheistic faiths is the transformation of Cushitic clan founders into religous and saintly figures of the concerned Abrahamic faith. So for the Agew, Agew clan founders transformed from Cushitic dieties and saints to Christian saints. For the Somali, the Somali clan founders transformed from pagan Somali saints to Muslim Arabian aristocrats who were 1st cousins of the prophet Muhammad. For Jewish groups, like the Beta Israel, the clan founders became biblical figures. Hence, a realignment of the clan founders and their status to fit in with the adopted Abrahamic faith is a common theme of pagan Cushitic-Abrahamic faith syncretism. Hence, the sort of pagan substratum of pagan Indo-European faiths with adopted Abrahamic faiths is very uncannily similar in this respect.