1. We can say it is correct but see down signed with *
2. Little different word order: Želim kupiti knjigu danas, a on je želi kupiti sutra.
Even much naturaly is if you put "ali" instead of "a": Želim kupiti knjigu danas, ali on je želi kupiti sutra.
* somebody says "ju" instead of "je" (grammar has some rules for this). Želim kupiti knjigu danas, a (or ali) on JU želi kupiti sutra. Anyway, we don't see much sentence with "ju"; it's normal to use "je". So, you shouldn't bother with this. :) I hope this didn't confuse you.