How can I trill difficult notes on the flute?

I’ve started practicing a piece that has about six different trills in it. Some are easy, because the fingerings are only one or two keys off from one another. But at least two (the best example being a high C to a high D) are really, really hard to trill quickly, even if I manage not to drop my flute.

Can any flautists give me some help?

The C-D trill is played by fingering a C and trilling with the D trill key, which is the small key between the E and F keys.

Here’s a good fingering chart that includes all trill fingerings. Note that contrary to what I said above, they recommend the D# trill key for a high C-D trill, as the D is more in tune that way.