I know that there's Rod of the Pact Keeper for Warlocks specifically, and I know there are items that increase spell attack rolls. Are there any feats, items, or other options in any of the official books that could be used to raise the saving throw DC of a character or is Rod of the Pact Keeper the only item they made for that?
The only other official way to boost your spell DC (without just boosting your ability score) is the Robe of the Archmagi, a crazily powerful legendary item.
The Lore Mastery Arcane Tradition, from Unearthed Arcana, gains the Alchemical Casting ability at 6th level. Among other things, it allows them to sacrifice a 3rd-level spell slot while casting a spell to boost the DC of that spell by 2. Note that as Unearthed Arcana, this is not official, and this particular Unearthed Arcana is widely considered to be extremely overpowered. I don't recommend using it, but I wanted to have something in this answer other than the Robe of the Archmagi.
Tasha's Cauldron of Everything introduced several new class-specific magic items that do this
Tasha's Cauldron of Everything has several magic items which give bonuses to spell save DC. Most notably there are six magic items which are patterned similarly to the Rod of the Pact Keeper, giving +1, +2, or +3 to both save DC and spell attacks plus an additional feature, as well as explicitly acting as a spellcasting focus unless that property is inherent to the type of item. These items collectively give options to every caster class (but not the Arcane Trickster or Eldritch Knight).
- All-Purpose Tool for Artificers, also granting temporary access to any cantrip
- Amulet of the Devout for Clerics and Paladins, also giving an extra use of Channel Divinity once per day
- Arcane Grimoire for Wizards, also improving the Arcane Recovery feature
- Bloodwell Vial for Sorcerers, also restoring some sorcery points during a short rest
- Moon Sickle for Druids and Rangers, also improving healing spells
- Rhythm-Maker's Drum for Bards, also recovering a use of Bardic Inspiration once per day
(The drum and concertina are musical instruments, so both should also work as a spellcasting focus even though it isn't mentioned in either item's description.)
Constant, Scaling Bonus
The only other item that boosts spell save DCs by a constant amount is the Robe of the Archmagi (DMG 194), which gives a +2 to spell DCs and attack bonuses.
Effectively increase DCs by using items with fixed DCs
Depending on what your save DC is, you could use various magic items to increase your save DC on certain spells.
For example, if you feel like taking a risk, you can try to cast a spell from a spell scroll that's a higher level than you can ordinarily cast (DMG 200):
If the spell is on your class's spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determ· whether you cast it successfully. The DC equals 10 + spell's level.
The table in the description shows that spells cast at higher levels have fixed DCs, so if you cast a 7th level spell from a scroll, its save DC is always 18.
Likewise, many (but not all) magic items usually have fixed DCs for the spells that you can cast using them. For example, the Helm of Brilliance (DMG 173) has a DC of 18 for all of its spells regardless of the caster's stats:
You can use an action to cast one of the following spells (save DC 18), using one of the helm's gems of the specified type as a component: daylight (opal), fireball (fire opal), prismatic spray (diamond), or wall of fire (ruby).
In this way, if you can get your hands on these magic items, you can effectively cast specific spells with a higher spell save DC. This strategy works best if you can get these items at lower levels, if you're multiclassed, or otherwise have lower stats.
Few magic items increases the DC by a flat amount.
Robe of the Archmagi, DMG page 194:
Your spell save DC and spell attack bonus each increase by 2.
There are some magic items which can impose disadvantage under certain circumstances, effectively increasing spells' DC.
Instrument of the Bards, DMG page 176:
When you use the instrument to cast a spell that causes targets to become charmed on a failed save, the targets have disadvantage on the saving throw.
As others have mentioned, there is the robe of the archmagi and rod of the pact keeper - but you can add to that list the ioun stone of mastery, which increases proficiency bonus so it stacks with those.
Wizards of the Coast has been careful to make items that increase save DCs rare. The warlock gets the rod of the pact keeper because at most they are casting 2 spells that require a spell save DC per short rest, unlike a wizard, sorcerer, or cleric that can spam a whole bunch of them.
It seems Tasha's Cauldron of Everything added similar items as the rod of the pact keeper for most of the other casting classes (they all come in multiple rarities, granting a bonus ranging from +1 to +3):