I don't believe there currently is. But I do think it would be a nice feature to be able to prioritize "colored" enchants over non-colored. Keep in mind that with enchanting, green often gives skillups (in my experience, anyway).
maybe but sometimes yellow doesnt give a skillup especially when it is about to turn green...i would rather use the mats on an orange i know will give a skillup than a chance on a yellow or even less of a chance on green
More often than not, the resources for the orange enchant will cost 3-4 times the price of the yellow and 10 times the price of the green, where these will give skillups about 75% and 25%. Skilling up enchanting on oranges is, financially, a terrible idea.
To answer the question: No, there is currently no way to set the barker to only pick leveling enchants. I appreciate that this seems like an interesting feature, but I did write the barker to help me level an enchanter and although I though about this idea, it never actually proved worthwhile making the effort to implement for me. If you just set the price priorities high then the barker will favour the more expensive enchants that you have, which invariably are the leveling enchants also.
My tip is to forget about leveling via the barker. If you want to power-level enchanting then you have to accept simply throwing enchants away. This is feasible up to 220 or so, but after that, you may as well settle in for the long haul and use the barker to actually make money while leveling slowly.