You overstayed your US visa by less than six months which would mean you do not have a bar to entry even if you accumulated unlawful presence.
Under section 212(a)(9)(B) of the Act, an alien is inadmissible if the
alien has accrued a specified period of unlawful presence, leaves the
United States after accruing the unlawful presence, and then seeks
admission during the period specified in (either 3 years or 10 years
after the departure, depending on the section 212(a)(9)(B)(i) duration
of the accrued unlawful presence)
(B) ALIENS UNLAWFULLY PRESENT.-
(i) In general.-Any alien (other than an alien lawfully admitted for
permanent residence) who-
(I) was unlawfully present in the United States for a period of more
than 180 days but less than 1 year, voluntarily departed the United
States (whether or not pursuant to section 244(e)) prior to the
commencement of proceedings under section 235(b)(1) or section
240, and again seeks admission within 3 years of the date of such
alien's departure or removal, or
Also you were on a J visa which typically have Duration of Stay hence you did not accumulate unlawful presence during your overstay.
Thus from your 214(b) denial it appears the consular is not convinced you do not plan to immigrate to the USA. It would appear this is directly related to your overstay. Almost thing happened to me in 1999 where although I did not overstay, I spent more time than I told the consular officer I would at the interview.
You are married with children and already established in your country and hence there is not much you can do to improve your situation, it is already good.
You can either get an immigration lawyer to apply on your behalf (not much they can do considering your situation) or wait a few more years and reapply.