Inferring birds such as darwins finches are adapted to occupy highly specific niches. would this adaptation make it easy or difficult for such birds to adapt to environmental changes?

Difficult, it has a highly specific niche meaning it needs very specific conditions to be satisfied and those conditions are probably rare.

Yes, over a period of time, and a few generations later, the birds would eventually adapt to the new situation. During Natural Selection, only the fittest that are best able to handle the change in environment will survive and pass on those traits that make them immune or resistant to the change, to their offspring.