I don't know the circumstances surrounding Texas' decision to secede in the ACW, but maybe if you have more pre-war German immigration (the Germans were generally anti-slavery), and further, those immigrants clustered in the Hill Country or around El Paso, you could have a West Virginia-style counter-secession.
Earlier, a different settlement to the Oregon Territory (both Washington, Oregon and/or Idaho admitted as states right away instead of Washinton remaining a territory until 1889 and Idaho until 1890) could result in an increased number of free states, which pre-war would mean a need for a corresponding increase in the number of slave states. Postwar, (assuming that Reconstruction and Jim Crow proceed as OTL) when both resulting states are readmitted to the Union, the Southern Democrats would have two more Senators to obstruct civil rights legislation, and perhaps tip the 1968 election from Nixon to Humphrey, since there will probably be two to four more Wallace electors (of course this timeline probably butterflies away the career of LBJ, but the issues of the time would probably be roughly equivalent and someone like Wallace would likely arise for racist sentiment to coalesce around).
Depending on where the intra-Texas borders are, the early 1900s oil strikes will probably only benefit the state in whose territory the derricks happen to sit, and a correspondingly smaller state government is easier to corrupt. So you might wind up with an ultra-rich West Texan oil oligarchy with a poorer eastern neighbor. Houston, being the last inland city accessible by sea, however, would still probably become a wealthy energy hub.