RAW you seem out of luck.
Extra channel only affect a paladin able to channel positive energy.
Vindicator's shield works channeling positive or negative energy, and while Earth Channel is similar, it is neither.
Same goes for the channel energy of the holy vindicator. Having Earth Channel your paladin levels lack the channel energy class feature, thus the HV levels don't stack. So the increase from the prestige class is limited to your cleric level.
I'm with Harald on this one. RAW none of those would stack with Stonelord.
Of course ultimately, it's up to your GM.
For point of reference though, if you have something that "could" increase two different abilities, you usually have to pick one and apply it to that. So in this case the Holy Vindicator would stack either with your Paladin's channel energy, or your Cleric's, not both.
Relevant quote from FAQ: "Channel Energy: If I have this ability from more than one class, do they stack?
No—unless an ability specifically says it stacks with similar abilities (such as an assassin's sneak attack), or adds in some way based on the character's total class levels (such as improved uncanny dodge), the abilities don't stack and you have to use them separately. Therefore, cleric channeling doesn't stack with paladin channeling, necromancer channeling, oracle of life channeling, and so on."
Personally I'd be fine with it as well :-)
Note, I don't play PFS myself. But my answer is based on the expectation that you risk running into a GM that sees it differently, given that the rules strictly as written doesn't allow it.
I am not sure what the chances are to get an official response in the PFS forums (but I guess pretty difficult). Yet, that might be your best bet, I you want to play the character without risking to meet a GM saying no.
I'd probably let it work as well, I'm just saying RAW it probably wouldn't apply.
The vindicator’s class level stacks with levels in any other class that grants the channel energy ability.
This is probably one of the most vaguely worded versions of this type of script. Normally with an ability like this, it forces you to pick between one of the others. So I guess this one one might apply to both, since it doesn't specify "positive" or "negative" channel energy. However Stonelord's ability isn't called Channel Energy, it's simply "Earth Channel", which would mean it would be a different ability, and thus would not stack with Holy Vindicator, since the ability explicitly states that a Stonelord loses the channel energy ability.
Again, this is simply my RAW interpretation.