Well Newfoundland had a limited interest in Confederation initially. The Newfoundland government wasn't a part of the Charlottetown Conference in September 1864 (which included from PEI, Nova Scotia, New Brunswick and the province of Canada (ie Ontario and Quebec when they were a single political unit with a united legislature)). However, Newfoundland did send representatives to attend the Quebec Conference in October 1864, albeit as observers rather than voting delegates. The representatives from the Newfoundland government became interested in Confederation and debated the issue the Newfoundland legislature.

Some politicians in Newfoundland were concerned that Confederation would lead to Newfoundland being subject to the disproportionate influence of Ontario and Quebec, which did not bode well with some in Newfoundland who held anti-French, and some anti-Catholic views and were worried since Quebec (formerly lower Canada) had the largest population at the time it would make Newfoundland less British and subservient to the interests of the majority in Confederation. Other issues included fears over higher taxes and worries about the introduction of conscription. As well, Confederation was considered to be bad for Newfoundland businesses which wouldn't necessarily be able to compete with those in Confederation, and there were concerns about higher taxes on fisherman.

Newfoundland did elect a pro-Confederation government in 1865 but it's legislature was never able to agree to Confederation. There was not that much support for Confederation among the general public for Confederation in 1867 (when Canadian Confederation occurred and 1869 when it was still an option on the table). Newfoundland at the time was a pretty isolated and politically separate colony that was, like a lot of colonies in Canada, not especially keen on being anything other than self governing (at least for domestic issues) and retaining a British identity. It should be noted that at the time Newfoundland was reasonably prosperous and there were strong opponents against Confederation in Nova Scotia and New Brunswick but they weren't as successful in opposing Confederation.

Confederation in Canada was primarily and financial tool, at least according to some scholars so provinces could consolidate debt, build railroads and a other industries, create a market for Canadian producers, and to be not American. The British were keen on Confederation as it greatly reduced and then practically eliminated the standing British military presence and it's according budgetary cost by making Canada responsible for it's own defense spending (at least in the immediate sense). Confederation also helped the Canadian financial industry a lot by enabling it to invest in westward expansion. As you can see, none of this seemed especially appealing to Newfoundland which is basically a rock on it's own with some sparsely populated territory to go wit it.

Newfoundland had considered Confederation again in 1895 but Canada wasn't interested as Newfoundland was primarily interested in joining Canada due to a bank crash that had occurred in Newfoundland.

Newfoundland as a result remained a British holding until 1949 when it ran again into some financial hardships and Canada was sort of the most logical option. As a result a referendum was held in 1949 which led to the province joining Canada.

This link provides a brief overview and googling Newfoundland and Confederation should help you out there.

Feel free to ask me any follow up questions.