On February 1st, 1861 a travesty was wrought. Texas chose to secede from the United States of America and thankfully such secession would end in a matter of years. So what if Texas never seceded from the Union, if it stood by America as the United States had stood by them? What impact both upon the Civil War and it’s aftermath does that create as well as the state of Texas itself? (Aside from Sam Houston being extremely happy with the loyalty to America being shown).
I agree with what others have said, you need to find a reason for Texas to remain that works very heavily against the deep South interests in play in 1860. One of the more interesting things to look at is an 1860 census from Texas. One of the fields that people provided information on was their place of origin. According to that census Texas was very heavily populated by people from the deed South. Not that you didn't have people from the North or from Europe, but demographically, they were swamped by Alabamans, Georgians and Mississippians.
If you can figure out a POD that would allow you greater foreign immigration or more heavy settlement by Northerners, then you could find a reason for Texas to remain or to sit it out. But to get a different outcome, you need different inputs.
One thing I'd point out, when Lincoln promised Sam Houston 50,000 soldiers to hold Texas in the union, there were several valid reasons that Sam Houston, loyal to the Union though he was, didn't accept it. First was this: Lincoln was promising something in 1861 that he didn't have the means to deliver. And two, any force Lincoln would have sent would have been at the end of a very long and tenuous supply chain. IOTL, there's a reason that even though Union forces captured Galveston in Dec 1862, they weren't able to keep it.
I've contemplated a TL in which Texas secedes but doesn't join the Confederacy, but it's hard to figure out how Sam Houston could have pulled that off, even if he were of a mind to do so... again, different outcomes require different inputs.