Britain does not give up the Mosquito Coast Protectorate in the 1860s, but retains and strengthens it. Perhaps there's some idea about a base for a canal across Nicaragua, but this never comes to anything. Nicaragua and Honduras don't like it, but they're too poor, weak and backward to do anything about it. The old Mosquito Kingdom expires in the early 1900s, and Britain takes a more hands-on, colonial approach. There is some black immigration from the West Indies, but except in a few areas it's mostly absorbed by the Miskito. Missionary societies are using the Miskito language in evangelising, and very slowly a small but growing educated elite is formed.
With the end of colonialism the protectorate becomes independant as the 'Republic of Miskitia' during the 1960s. Nicaragua protests, but with international recognitiomn can do nothing. (cf Belize and Guatemala) Today Miskitia is a sleepy, rather backward Caribbean country that is a member of the Commonwealth and plays cricket. It's just that the majority of the population and the dominant group are indigenous Americans with their own traditions, and their language, Miskito is widely used and is co-official with English.