Ships & Modules

As has been pointed out there are a handful of armor tanked ships that can fit launchers and even less that do it particularly well although ships that fit both armor and missiles have to be designed for it to some extent because of fittings.

Launchers are heavy on CPU use and lighter on PG and this is also true of shield mods meaning Caldari for example are CPU rich but a little bit PG challenged. This also means that fitting armor tanks to a ship that is traditionally shields and missiles will often run into fitting issues from its lower PG.

Conversely trying to fit launchers to a traditional armor tanker (excluding things like Legion/Sac that were designed with that combination in mind) tend to run into CPU issues as soon as you start fitting anything beyond the launchers and tank.

It's not that you can't make functional fits that are that far outside the box, it's just that particularly with trying to fit missiles to an armor tank whether you are putting missiles on an armor ship that doesn't have missile bonuses or putting an armor tank on a traditional shield tanker will often require sub-optimal downgrades of fittings somewhere in order to fit into whichever fitting constraint you happen to have when you are not using one of the Amarr ships designed to do armor and missiles.

You know what, that may be the best option. It even has a missile damage bonus.
Though it comes with a shield boost bonus, it has 5 lows, so it should be armour tankable.