Hi Rajkumar !
Best to my knowledge, MDF can be very well laminated using formica/sunmica using fevicol.
There might be a reason your carpenter is saying no.... reason could be, due to white fevicol which is water based, MDF may change its shape, mostly after applying fevicol and formica, MDF tend to turn little curvy.
Then another option is rather than using regular fevicol, it can be pasted using fevicol SR, it is synthetic based bonding agent and it dries fast and lasts equally good.
another option as suggested by Fantastic, spray painting it, either you use duco paint (used for car's body painting) but as said its time and effort taking. If not duco, then spraying luster also works fine but you wont get much glossy finish, but lasts long. i have luster roller painted floor standing. But are semi gloss.
One more option is buying a vinyl laminate, many color options are available and its kind of sticker which you paste on MDF. you can check diyaudiocart.com or ebay.in as well.
I have seen vinyl laminated speakers and look equally nice.
Hope something works for you out of these options.
Best Regards
Rahul