By the rules
According to the rule book, in the Assigning the Gods section, the DM is supposed to start this process by putting out as many god cards as there are players. Technically, the game would stall at this point. Eliding that little problem, you'd end up with the person or people who happened to roll worst not having a god card.
However, as you point out, this seems like it might be unsatisfying. Here are some approaches to how you might handle it and how they (or similar things) worked out in my games.
Roll with it
Since the gods hate you, none of them favor you. Better luck next time. I think this works out from two different examples.
First, no game has an equal balance of gods between the players. Only in the case of seven players do they even have the same number of gods each. Surely even then, the gods are called on at different rates. This setup has an inherent tendency to self-balance. The more spite each god spends, the more players fail, the less spite the gods get.
Second, I once ran a game wherein a player used spite exactly once. She had earned more than a dozen by the end of the game. It didn't impact her orks at all compared to the other players'. This may be because the antagonism dynamic in the group was Team Gods vs. Team Orks, up to and including players spiting their own orks. There was zero antagonism between players per se. In this scenario, I would say the same overall spite was spent as compared to my other experience, due to the above-mentioned feedback loop.
If your table tends to be more player-player adversarial (as if their ork(s) could somehow win), this route is much less likely to work out.
Find a new god
Make a new god by either splitting responsibilities of an existing one or defining a new category. Throwing came up a good amount in the games I've run, and it was often a toss up between Pounding Stone Lifting Rock and Slashings and Slayings.
I considered making this official to balance out two gods per player in a four man game, and opted not to. From a game play perspective, I as DM found myself wishing there was one more often than I ended up calling for the gods that were used less, such as the un-orky Lying Tongue Twisting Words and the cowardly Sneekings and Peekings. There's definitely enough room for more gods in the pantheon if you feel the need to balance out actions taken. It would reduce the spite from the more heavily used gods, but would give potentially more spite under the succeed-with-your-own-god rule.
Pool the spite
Consider sharing the decision making between all the players, and giving each god their own spite pool. This is more or less how my tables ended up running anyway. My players spontaneously decided to role play reasons for why their god was adding spite to any given roll. Maybe three quarters of the rolls went unremarked, while the others all solicited some commentary or other about why a god wouldn't like it. The players would happily suggest reasons various gods would add spite, regardless of the controlling player. The commentary worked best when the ork and I were very descriptive about what was happening, and the players all maintained an non-adversarial mindset. I did notice the more outgoing and enthusiastic players more often suggest things, and thus got their ideas implemented. This didn't seem to be a problem for anyone at the table.
Share the hate
On the less supported-by-experience side, you could allow the gods to capriciously change players. There are a number of options here.
- Rotate once in a while (say, every half hour or scene break)
- Rotate any time they're used
- Redo the Assigning portion halfway through the game, in the reverse of the original dice order.
You could also have a god's spite tokens move with him, but I'd recommend letting players keep the spite they've earned.
Unfortunately, the closest experience I have to this is when one player left the room. Their god was called for, so I just had the player seated next to him choose instead. The absent player got the spite for success, and there was no notable side effect (either in game or socially at the table).