Texas petitions for unqualified parties to obtain a place on the ballot may start to circulate on March 9. They are due May 22. Past print issues of Ballot Access News have said the deadline is May 16, but that is incorrect, and this error will be corrected in future issues.
The only unqualified parties entitled to circulate a petition this year in Texas are the Constitution, Reform, Veterans, Christian, Modern Whig, and Socialist Parties. They are the only ones who filed the declaration of intent by January 2, 2016. The constitutionality of the January 2 deadline for doing that has never been adjudicated in court. At least as it relates to presidential elections, it is probably unconstitutional.
Newly-qualifying parties need 47,086 signatures. The Libertarian and Green Parties are already on.
Texas independent candidate petitions are due June 30, unless they are for president, in which case the deadline is May 9. It is very likely the independent presidential petition deadline is unconstitutional. There is no state interest in letting non-presidential independents have until June 30, but saying independent presidential candidate petitions are due May 9. Thanks to Jim Riley for some of the information in this post.