There are many companies that sell high tech, precision needles, but if you want to start off at very low cost, you could make one yourself in an hour or two using three hypodermic needles, a Dremel type or other cut-of wheel and a bit of epoxy glue. One of my students made one and successfully spun coaxial fibres using this approach. Take a 15G needle and cut to 31mm overall (outer tube); take a 22G needle and grind down the 4 flanges on the outside of the luer connector so that they fit snugly into the back of the 15G needle when the former if fed through the latter. Cut off the inner needle so that it protrudes about 0.6mm from the outer. Finally, take a 22G needle and use it to "drill" a hole into the side of the 15G needle Luer connector, cut off its tip and then reinsert (at right angle) and glue into place with some epoxy, Also use epoxy to glue the 15G and 22G needles together where they meet at the luer fittings. Centre everything and let the glue set. Pump the core fluid through the 22G needle and the shell through the 18G side arm that connects with the anulus between the 15G and 22G needles. Of course this is an example of gauges to use, but it can be adapted as needed.
rame-hart is the world's largest producer of coaxial needles used for electrospinning. They offer prebuilt coaxial needles as well as custom made coaxial needles. See http://www.customspinnerets.com/coaxial for information on configuring and ordering.