K. - here is the link you need to the Texas Dept. of Health - http://www.dshs.state.tx.us/immunize/school/default.shtm
There you'll find the official affidavit and instructions on what to do with it. You can get the affidavit for "reasons of conscience" (which is what the religious belief falls under).
An official affidavit is acceptable for enrollment, but do know that only schools that receive state funding are required to accept an affidavit in lieu of vaccination records. Any private school, which includes the majority of daycares, may refuse admittance, regardless of the reason (medical, religious, etc.).
You might try calling the corporate offices of some of the chains ahead of time and finding out what their policy is. The request is highly uncommon at a daycare level, and the director may be unsure what to do, and that will frustrate you as you're looking for a good center - and you may even get varying answers from different locations of the same chain. If you know ahead of time that, say, Creme de la Cremes will accept the affidavits, then you can feel more confident about even beginning the enrollment process.
Good luck!
S.