I am sending you the pronunciation guide here. If you need an audio file, let me know your email address and I'll send one.

Ku - rhymes with "ku" of "kudoz"
ri - rhymes with "re" of "recycle"
gram - rhymes with "gram" or "kilogram"

Please find (play or download) a small mp3-file for "Kurigram" at this URL: http://www.box.net/shared/zybvijt5va . (The word is repeated once)

Kurigram is the name of a district in Bangladesh. Mr. Saleh Chowdhury is right about the pronunciation, in that :

Ku - rhymes with "ku" of "kudoz"
and
gram - rhymes with "gram" or "kilogram" (or telegraph).

But,

the 'r' in Kurigram does NOT exactly sound like the letter 'r' in English (e.g in 'Recycle'). Please notice this in the audio file. Although there is some similarity, the difference is significant too. Mr. Chowdhury or others posting replies here are not wrong -- there is simply no letter in the English alphabet that can accurately represent this sound. Pronouncing it like the English 'r' can be an easy solution for a foreigner though, unless he/she can master the correct pronunciation.

May be the 'r' in 'Kurigram' can be called some kind of an opposite of Affricate or a "palatal flap" (although the IPA symbol used for this is a retroflex flap, but in reality it seems more palatal to me) ? It begins as a palatal approximant - the back (not the tip, as in English 'r') of the tongue approaching but not exactly touching the hard palate (as opposed to the alveolar or post-alveolar 'r' in English), and then in quick succession ending as a brief plosive or flap consonant- the back of the tongue hitting the hard palate for a fraction of a second and releasing/interrupting the air gathered/flowing during the pre-flap approximant phase.

This is of course my understanding of the mechanism and not from a standard text/resource on Bengali phonetics.