If our judge finds a defendant guilty of criminal contempt (non-child support case) and sentences the defendant to the max 180 days; is there any authority allowing the Judge to probate the sentence?

I don't think so. Probation is only authorized by 42.12, and that article specifically limits it to being imposed "upon conviction." Entering an order of contempt isn't the same thing, in my opinion.

Actually the judge can probate part or all of the criminal contempt sentence. The court has inherent authority to enforce its orders. Ex parte Gorena 595 S.W.2d 841 (Tex. 1979) A criminal contempt order is considered quasi-criminal meaning that the court should follow the criminal guidelines where possible. Ex parte Johnson 654 S.W.2d 415 (Tex. 1983). Even the United States Supreme Court recognizes that a criminal contempt sentence can be probated. Muniz v. Hoffman 95 S. Ct. 2178 (1975). Naturally, this only applies to the Court's general inherent power of enforcement. If a statute applies to a particular circumstance and the statute provides for contempt enforcement but does not allow for probation then the court must follow the statute in that case.

The Supreme Court case you cited was regarding a specific federal statute. Of course if a statute authorizes probation for contempt then it can be granted. The court's inherent authority to enforce its orders is how it has power to issue contempt judgments at all, but that doesn't independently give it authority under 42.12. And the quasi-criminal nature of contempt gives it due process and similar protections. But given that probation in Texas is authorized under a particular statute only and that doesn't encompass contempt findings, I have my doubts as to whether that statute can be applied in contempt cases. I haven't found any Texas cases that applied it, though my search was pretty quick.

Suspend yes, an inherent power. For punitive contempt. For coercive contempt (ie: give your source or go to jail) the sentence ends when the contempt ends as found in the sole discretion of the court.

Probation (with supervision and fees etc), no only for criminal convictions.

The problem here is language not power.