Argirios Pagartanis sent me a link to source [12] (list of sources is on the Congo Departments page). It lists district populations, except for the arrondissements of Brazzaville and Pointe-Noire.

The Republic of Congo is divided into twelve departments. Each department is subdivided into districts and communes, except Brazzaville and Pointe-Noire, which are subdivided into arrondissements. There are 86 districts, 4 communes, and 11 arrondissements at present. The districts are also called sous-préfectures (sub-prefectures).

As often happens, I have several sources for the districts of Congo, and they disagree with each other. Originally, I used the districts on the Secondary Administrative Level Boundaries site (source [13]). I have now updated it using source [2]. The difference between the two sources is that the second one adds four autonomous communes, and four arrondissements of Pointe-Noire. I think the communes were there all along. The reason for adding the arrondissements is that Pointe-Noire has now become a separate department, so its subdivisions are now secondary subdivisions of the country. I've also changed the middle two letters in the HASC codes to reflect that change.

This map  shows what was apparently an earlier set of districts, with indications of new districts added.

District	Type	HASC	Population
Abala	d	CG.PL.AB	11,296
Allembé	d	CG.PL.AL	4,640
Bacongo	r	CG.BR.BA
Bambama	d	CG.LE.BA	4,906
Banda	d	CG.NI.BA	6,910
Bétou	d	CG.LI.BE	29,736
Boko	d	CG.PO.BO	13,643
Boko-Songho	d	CG.BO.BS	12,575
Bouaniela	d	CG.LI.BO	7,084
Boundji	d	CG.CU.BO	16,015
Divénié	d	CG.NI.DI	13,549
Djambala	d	CG.PL.DJ	17,265
Dolisie	c	CG.NI.DO	83,798
Dongou	d	CG.LI.DO	19,365
Enyellé	d	CG.LI.EN	21,193
Epéna	d	CG.LI.EP	17,499
Etoumbi	d	CG.CO.ET	12,387
Ewo	d	CG.CO.EW	20,195
Gamboma	d	CG.PL.GA	43,221
Goma Tsé-Tsé	d	CG.PO.GT	15,615
Hinda	d	CG.KL.HI	32,995
Igné	d	CG.PO.IG	29,290
Impfondo	d	CG.LI.IM	47,951
Kakamoéka	d	CG.KL.KA	7,817
Kayes	d	CG.BO.KA	13,123
Kéllé	d	CG.CO.KE	15,205
Kibangou	d	CG.NI.KB	17,928
Kimba	d	CG.PO.KM	4,516
Kimongo	d	CG.NI.KM	19,578
Kindamba	d	CG.PO.KD	17,295
Kingoué	d	CG.BO.KI	11,910
Kinkala	d	CG.PO.KK	34,608
Komono	d	CG.LE.KO	14,581
Lékana	d	CG.PL.LE	16,761
Liranga	d	CG.LI.LI	11,287
Loandjili	r	CG.PN.LO
Londéla-Kayes	d	CG.NI.LK	8,150
Loudima	d	CG.BO.LO	32,775
Louingui	d	CG.PO.LG	10,553
Loukoléla	d	CG.CU.LO	21,442
Loumo	d	CG.PO.LM	4,715
Louvakou	d	CG.NI.LO	13,408
Lumumba	r	CG.PN.LU
Mabombo	d	CG.BO.MB	11,839
Madingo-Kayes	d	CG.KL.MK	13,290
Madingou	d	CG.BO.MD	62,800
Makabana	d	CG.NI.MK	14,164
Makélékélé	r	CG.BR.MA
Makotipoko	d	CG.PL.MA	18,756
Makoua	d	CG.CU.MA	21,910
Mayama	d	CG.PO.MA	7,036
Mayéyé	d	CG.LE.MA	13,649
Mayoko	d	CG.NI.MY	5,147
Mbama	d	CG.CO.MA	8,040
Mbandza-Ndounga	d	CG.PO.MN	9,737
Mbinda	d	CG.NI.MB	4,783
Mbomo	d	CG.CO.MO	7,163
Mbon	d	CG.PL.MB	3,163
Mfilou	r	CG.BR.MF
Mfouati	d	CG.BO.MF	29,931
Mindouli	d	CG.PO.MI	53,584
Mokéko	d	CG.SA.MO	30,172
Mossaka	d	CG.CU.MO	25,636
Mossendjo	c	CG.NI.MO	13,238
Moungali	r	CG.BR.MO
Moungoundou Nord	d	CG.NI.MN	1,385
Moungoundou Sud	d	CG.NI.MS	5,703
Moutamba	d	CG.NI.MT	10,385
Mouyondzi	d	CG.BO.MO	36,815
Mpouya	d	CG.PL.MP	9,283
Mvoumvou	r	CG.PN.MV
Mvouti	d	CG.KL.MV	18,094
Ngabé	d	CG.PO.NG	30,091
Ngbala	d	CG.SA.NG	4,613
Ngo	d	CG.PL.NG	16,751
Ngoko	d	CG.CU.NG	2,866
Nkayi	c	CG.BO.NK	71,620
Ntokou	d	CG.CU.NT	4,075
Nyanga	d	CG.NI.NY	9,340
Nzambi	d	CG.KL.NZ	3,137
Okoyo	d	CG.CO.OK	10,009
Ollombo	d	CG.PL.OL	21,272
Ongoni	d	CG.PL.ON	12,183
Ouenzé	r	CG.BR.OU
Ouesso	c	CG.SA.OU	28,179
Owando	d	CG.CU.OW	40,174
Oyo	d	CG.CU.OY	17,948
Pikounda	d	CG.SA.PI	3,513
Poto-Poto	r	CG.BR.PP
Sembé	d	CG.SA.SE	9,550
Sibiti	d	CG.LE.SI	46,608
Souanké	d	CG.SA.SO	9,711
Talangaï	r	CG.BR.TA
Tchamba Nzassi	d	CG.KL.TN	16,622
Tchikapika	d	CG.CU.TC	5,978
Tié-Tié	r	CG.PN.TT
Tsiaki	d	CG.BO.TS	11,315
Vindza	d	CG.PO.VI	5,912
Yamba	d	CG.BO.YA	14,370
Yaya	d	CG.NI.YA	3,805
Zanaga	d	CG.LE.ZA	16,649
Type: c=commune, d=district, r=arrondissement. HASC: Hierarchical administrative subdivision codes. The middle two letters indicate the department. See Departments of Congo page for codes. Population: 2007-04-28 census. Capitals have the same names as their districts.

Other names of subdivisions:

These are names that I've seen on various websites. Some of them may be outright mistakes.

1. Allembé: Alembé (variant)
2. Bouaniela: Bouagnela, Bouanéla, Bouanila (variant)
3. Enyellé: Enyelé (variant)
4. Goma Tsé-Tsé: Ngamaba (obsolete); Ngoma Tsé-Tsé (variant)
5. Hinda: Loandjili (obsolete); Minda (variant)
6. Igné: Ignie (variant); P.K. 45, PK Rouge (obsolete)
7. Kakamoéka: Kakamoueka, Kalamoéka (variant)
8. Kayes: Nkayi (obsolete)
9. Kéllé: Kélé (variant)
10. Kimba: Kibouendé (variant)
11. Louvakou: Dolisie (variant); Loubomo (obsolete)
12. Madingo-Kayes: Madingou Kayes (variant)
13. Makotipoko: Makotimpoko, Mokotipoko (variant)
14. Mayéyé: Makabana (variant)
15. Mbandza-Ndounga: Mbanza-Ndounga (variant)
16. Mokéko: Ouesso (obsolete)
17. Moutamba: Mossendjo (obsolete)
18. Mvouti: Mvoun (variant)
19. Ntokou: Niokou, Tokou (variant)
20. Nyanga: Nianga (variant)
21. Ongoni: Ongogni, Ongonyi (variant)
22. Pikounda: Pikoundo (variant)
23. Tchamba Nzassi: Nzassi, Pointe-Noire, Tchiamba-Nzassi, Tsama-Nzassi (variant)
24. Vindza: Vinza (variant)

Change history:

Again, we get differing information from different sources. According to a report from the Ministry of Health and Population  dated December 2003, Congo is divided into eleven administrative departments, and further into 76 sub-prefectures and six urban communes: Brazzaville, Pointe-Noire, Dolisie, Nkayi, Mossendjo et Ouesso. Each urban commune is again subdivided into arrondissements. This government site , citing "Atlas Congo" (Éditions du jaguar) as its source, shows these changes in 1984 and 1994:

1. 1984: Ngamaba district moved from Brazzaville to Pool and renamed Ngoma Tsé-Tsé; Loandjili district split from Pointe-Noire and renamed Hinda; Loubomo district renamed Louvakou; Mossendjo district renamed Moutamba; Nkayi district renamed Kayes; Ouesso district renamed Mokéko.
2. 1994: Cuvette-Ouest region split from Cuvette (effective 1995-02-18), consisting of Etoumbi, Ewo, Kéllé, Mbama, Mbomo, and Okoyo districts; Bouaniela, Kimba, Moungoundou Nord, Ongoni, Tchamba Nzassi, and Yaya districts created; status of all "postes de contrôle administratifs" (administrative control stations) changed to districts, including Banda, Igné, Louingui, Loumo, Mbinda, Mpouya, Ngbala, Ngo, and Nyanga. According to another source, Etoumbi, Mbama, Ngoko, Tchikapika, and Tokou were also P.C.A.s.
3. 2005: In Brazzaville département, Madibou and Nkombo-Djiri arrondissements created. In Pointe-Noire département, Mongo-Poukou arrondissement split from Loandjili; Ngoyo arrondissement split from Tié-Tié. However, the new arrondissements have not been implemented yet, as of 2010-02-22. Also in the waiting list is a plan for Île Mbamou to become a district of Brazzaville, and for Tchamba Nzassi to be reassigned from Kouilou département to Pointe-Noire.