While you can make variant constructs using animate object and permanency using the alternative construct creation rules, there's no provision for making super custom ones like the iron cobra.
While it's all on one page in the PFSRD, there are two fundamentally different rulesets at work here. One is originally in Haunting of Harrowstone, and that just lets you trade construct size, in the form of CP, for a limited set of abilities (grab, burn, etc.), and lets you stick permanency on them to keep them around. It's reprinted in Ultimate Magic.
Right after those rules in Ultimate Magic is a completely separate set of rules for building new constructs. Those rules use CR - not CP - and have you basically just monster-build as a base. An iron cobra does not have '2 CP', it is CR2. There is no specific pointed-out list of all construct abilities. Only the ones listed in that first ruleset are allowed for the animate object-based creation. Anything in the MM or beyond is allowed for creating constructs, but that's basically like creating new monsters (and is subject to your GM approval).
So you can create a slightly varied animated object with animate objects and permanency, or you can create an iron cobra with Create Construct and the usual list of requirements.