Start by accepting that your deck won't be as straight-up competitive as it could be with Mox Opal — it's a staple, and cutting staples, especially for budget reasons, inevitably involves giving away some percentage points here or there. Maybe you can gain some improvements in unusual matchups, though.
What does Mox Opal do for you?
Consider what Affinity does, in general:
- Affinity is a fast aggressive creature deck
- Generally, Affinity is an "all-in" deck. The Affinity player wants to dump their hand onto the battlefield as quickly possible in order to power up a card like Cranial Plating. The deck mainly relies on speed to blank a lot of your opponent's card. You have a few cards to dig you out of a stall (Etched Champion, Thoughtcast) but you really aren't trying to grind down an opponent slowly.
- It plays a bit like a combo deck, sacrificing individual card power for massive synergy.
- There's significant redundancy in kill conditions. Cranial Plating, Ravager + Inkmoth, Signal-Pest-powered beatdown, &c. But your deck generally sucks if you don't have one of your key cards out.
So, what does Mox Opal do in that deck?
- It's an accelerator. You can use it to put a Cranial Plating or an Arcbound Ravager down on the field on turn 1.
- It's color-fixing in a deck that plays lots of colorless lands (up to 12) and 2-4 colors of spells. Don't underestimate the value of being able to make BB to move Cranial Plating around at instant speed, as well!
- It's an artifact. It ups your artifact count for Cranial Plating, Thoughtcast, and Etched Champion. You can sac it to Ravager. It'll keep your Glimmervoid from dying.
- It's free. You can dump an Opal onto the field without disrupting the flow of the rest of your turn.
- It's a non-creature artifact so it'll survive sweepers (besides the ones people sideboard specifically to hose you). I don't think that's as important right now, ever since Zoo pushed Pyroclasm out of the format.
That's a tough act to follow!
Here's my best shot.
The most important thing is to remember that consistently executing the deck's overall concept is more important than finding a direct functional replacement for the mana rock.
- The closest thing to Mox Opal in functionality is Springleaf Drum. You should be playing a playset of these already, though.
- You can also just add lands. Replacing 4 Opals with 4 lands won't do good things for your deck, of course, but you could totally add 1-2 lands. Gemstone Mine (already a staple) and City of Brass/Mana Confluence are decent picks for multicolor support.
- Paradise Mantle is a 0-cost card that's basically a worse Springleaf Drum. It's a bit harder to get explosive starts with it due to summoning sickness. The main knock against it, though, is that doubling up on Springleaf Drums stretches your creature base pretty thin. I'd playtest 2 rather than the full 4.
- Gitaxian Probe is a 0-cost cantrip. You can run these in the hopes of just getting to your other cards quicker. (It is way better for this purpose than Mishra's Bauble, which is an artifact but pretty terrible.)
- Chromatic Star is a bit slow for this deck but it might be a decent color-fixer in a pinch. It cantrips if you feed it to a Ravager, and it counts for Thoughtcast's affinity even if you sac it to make blue mana for the spell (because you calculate costs first, then pay them).
- Many Affinity decks already play a singleton Welding Jar. So try 1-2 and see how far that takes you. It's great for pushing through an Inkmoth kill.
- You can always just up the creature count and play it more like a beatdown deck. Affinity typically runs some mix of "lords" like Signal Pest, Steel Overseer, and Master of Etherium. Just add the one you don't have already. (If you have all of those already: did you take out Vault Skirge or something? Try putting that Vault Skirge back in.)
- You can experiment with maindecking hate cards, especially if you play in a relatively small and cozy environment where you know what decks you'll face:
- Spellskite and Phyrexian Revoker are nifty creatures that can mess up a lot of decks (Ethersworn Canonist, too, but you're cutting color depth so I'd stay away from colored artifacts).
- Relic of Progenitus is a great non-creature pick, since it cantrips and gives you splash hate against decks that run Goyf and Snapcaster.
- Pithing Needle and Grafdigger's Cage can also work if you really, really know your metagame well.
- Another way to maindeck hate is to add targeted discard in the form of Thoughtseize, Duress, or maybe Inquisition of Kozilek. Essentially you're accepting that your deck will be just a bit slower than the typical shell, but you're planning to make up for it by disrupting opponents more. You'll want to rejigger your mana to support more black sources to make this work, of course.
To reiterate: you'll probably want to add a land! Even if you go the Paradise Mantle route, none of these cards are quite as fast and flexible as Mox Opal, so you really do just want the extra land to smooth out mana production.
Note that you may need to adjust other cards if you're changing your ability to produce mana — not playing Mox Opal basically guarantees that you can't play the greediest of the Affinity lists.
Above all else, remember that, since there's no drop-in "next best" replacement, you're going to have to test and tune your deck.