Sorry for the bump, I missed this when originally posted.
The problem with the Texas dollar was that it was severely inflated, due to overprinting. Texas needed cash, but had no known reserves of precious metal. Making coins would have been hard (they had no minting facilities and no industrial base to create such facilities, so they would have had to pay a foreign mint, probably the US Mint, to design and make coins for them); making paper money was easy since all you need is a printing press and some ink. So they chose the easy route. Physical coins, and tokens, rely on the currency being stable enough that a coin isn't going to be rapidly devalued to the point of it being worth far more as scrap metal than as a face-value coin. The Texas dollar soon fell to being worth just a fraction of a US dollar; 1 Texas dollar was already "small change".
At times of inflation and financial instability, private low-value paper currency ("shinplasters") were used as coinage substitutes; these supplemented and eventually replaced the Texas redbacks and served as unofficial small change. The financial situation in Texas did not improve until after it joined the Union, so it never really had the chance to issue its own coinage.
Consider and compare the situation with the Confederate States, a couple of decades later. They had a much more developed industrial base, had some supplies of coinage silver, and even had inherited
a former Union mint in New Orleans with Louisiana joining the Confederacy. Yet Confederate coinage never got past the "design and pattern" stage, for much the same reason as coinage was never issued in Texas: economic instability and overprinting of Confederate money, causing the economy to become hostile to circulating coinage.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis