Nice photo. A few comments. First, there are no doubts that this is a coucal, they are distinctive and nothing else look alike. Furthermore, Burchell's Coucal isn't found in (or anywhere near) Nigeria so isn't a possibility. The White-browed Coucal (which is sometimes considered to include Burchell's; together they are also called Burchell's) comes "somewhat close", but the nearest record still is some 1000 km. away from Nigeria. Even if it had occurred, it has a very different head & mantle pattern (only "real Burchell's" of far SE Africa look similar). With that pattern there are two possibilities in Nigeria: The first has already been mentioned; Senegal Coucal (Centropus senegalensis). The second is the Blue-headed Coucal (C. monarcha). I don't personally have any experiance with last, but it doesn't look like any of the Senegal's I've seen in Kenya where the same subspecies is involved. The faint barring on the wing indicate that it is in the transition from immature to adult. Both species also have warmer buff underparts as immatures which could explain why the underparts seem likewise on this individual. The head does seem to be vaguely glossed with blue (again, presumeably less so than in full adults), which leads me to a tentative guess of Blue-headed Coucal in trasition from immature to adult. The Blue-headed also is slightly less rufous above and supposedly also warmer buff below (even as adults) than Senegal's, which again lead me in the same direction. It should be mentioned that Blue-headed Coucal is largely restricted to areas near water, and if your garden is far from any densely vegetated swampy area/river, it must be considered unlikely to occur; which then would lead you to Senegal. Do note that these species differ significantly in size, which could also lead you to a conclusion in case you noticed. Total lenght of Senegal Coucal is ~38-40 cm. versus ~46 cm. for Blue-headed.
In any case, you certainly can limit yourself to Senegal & Blue-headed Coucal.