For documentation purposes, you may use Enterprise Number 32473 (per RFC 5612). However, to my knowledge, there is no Enterprise Number allocated for purely private use, in the same way that the RFC 1918 IP address space was allocated. I read one argument in favor of this practice to prevent someone from implementing a private OID numbering for a tool that is then subject to use outside of their network, thus causing conflicts.
Instead, anyone who wishes to implement or use this number space should apply for their own Enterprise Number. There is no fee associated with it, and it usually only takes a few weeks to process. Simply submit your application request to IANA, and they'll allocate a number to you. Of course, before making that request, verify whether you or your company already have a number assigned. If so, then you should be good to go. You are free to utilize the branches underneath your Enterprise Number however you wish, so you have a virtually limitless space to work with.