My County Judge requested an opinion as to whether he may carry a concealed handgun in the courthouse. He is a commissioned peace officer. Has anyone already researched this issue? Don't want to reinvent the wheel. Thanks.

The answer is yes they can carry in the Court House so long as they have a valid CHL or other legal means of carrying.

Sec 411.201 of the Texas Goverment Code authorizes Judges to receive CHL's and under Sec 46.03 ( Places weapons prohibited) of the Penal Code, Sec 46.03(b) states: It is a defense to prosecution under Subsections
(a)(1)-(4) that the actor possessed a firearm while in the actual
discharge of his official duties as a member of the armed forces or
national guard or a guard employed by a penal institution, or an
officer of the court.

See PC 46.03 (a) (3) and 46.15 (a)(1): Peace officer may carry in places where carry is prohibited, including courthouse, regardless of whether the peace officer is engaged in the actual discharge of the officer's duties.

Is it a conflict of interest to be a commissioned peace officer and a County Judge?

I haven't kept up with this body of law, and more facts would be needed, but this may be a starting place:
A.G. Op. JM-1047 (1989): The common law doctrine of incompatibility prevents one person from serving as both JP and jailer in the same county. Also, the JP may not be a "neutral and detached magistrate" for the purposes of issuing arrest and search warrants, as required by the 4th amendment.

Under PC 46.15 (4), judges are exempt, as are District Attorneys, Criminal District Attorneys, and County attorneys.

46.15(4) only applies if they have a concealed handgun license under Subchapter H, Chapter
411, Government Code.