According to the instructions, you use the I-134 if you are not eligible to use the I-864. Specifically:
Form I-134 may be used in any case in which you are inadmissible on public charge grounds, but in which you are not required to have Form I-864 filed on his or her behalf. Section 213 of the Act (not section 213A) permits the admission of an alien who is inadmissible on public charge grounds, in the discretion of the Secretary of Homeland Security (or, for immigration judge cases, the discretion of the Attorney General) upon the posting of a bond or other undertaking (method). Form I-134, is the “undertaking” prescribed in section 213 of the Act.
Do not use Form I-134 if the alien whom you are sponsoring is required to have Form I-864 instead.
