I would suggest going to your local piercing shops and asking them who they know that makes custom jewelry. Some shops do their own or the artists will do it on the side. They often have to do this for things like industrials or other semi-unique peircings (surface bars) so they have the tools available. Not every shop does it, but shops all tend to know eachother from conventions and stuff so they can almost always point you in the right direction.
They might also point you to any local jewelry shop - many can make their own jewelry. It isn't a difficult piece... they just cut the barbell to the right length (basically a piece of wire), use a tool to thread the end, use a pre-made ball and then melt the jewelry on the other end. Might help if you could find any sort of phi piece.. maybe a keychain or bracelet charm? Then they just need to melt it onto the end of another ring. Pretty easy. They could make it for you, but you'd likely be paying quite a bundle for it. If you could get something like http://shop.ebay.com/i.html?_nkw=Phi+charm&_sacat=0&_trksid=p3286.m270.l1313&_odkw=Phi+bracelet&_osacat=0 they could likely take out the little Phi and use it.

I have bought custom made jewelry on ebay before - I needed white gold (allergies and hate the look of yellow gold) barbells in a very specific length and 14g... 9/16" is difficult to find as it is, nevermind in white gold. They cost me about 75 dollars for two.. however they're just standard barbell and standard balls. The only thing is they're not quite as perfect as factory pieces unless you are willing to pay. So mine have one ball mounted and the other threaded because it's easier for them, and the balls aren't quite round or threaded exactly in the center (ok otherwise unless your looking carefully). I THINK it was this shop http://stores.shop.ebay.com/Piercing-Buddies__W0QQ_armrsZ1 but I can't tell for sure as it was no longer saved in my history. If it is, they have a website they can point you to to put in your request - just email them and ask... if I find the shop I'll come back and let you know.

Good luck!

EDIT: Found it.... http://www.gracebodyjewelry.com/ ... they make all their stuff per order so they can likely do it for you, they're the ones that did my custom barbells.

If you REALLY get stuck, I have a friend in Toronto that also sells custom jewelry and she'll do any order.. she could do it for you but It'd be very basic. she'd likely get one of those charms on ebay (or talk to one of her other friends that do custom.. she's always trading jewelry parts with people all over the place), she'd remove the Phi piece, get a standard simple navel ring, remove the ball and melt it onto the end. It'd take awhile but I'm sure she could do it!

Any jeweller in India could make that for you according to your design. Should not be more than US$ 50 for a simple one like you want. Try Ebay. Or I could get you one made and send it over to you. :-)

I found a great designer, Mariposa Designs, to make you one in your price range if that is your preference.
Also found some links to existing sorority belly button rings that are reasonably priced and on sale.