The 5000 gp diamond is the only diamond on any of the DMG treasure tables.
As you have observed, the only diamond on the Gemstones tables in the DMG is the diamond appearing on the 5000 gp Gemstones table. If you are strictly using the treasure tables in Chapter 7 for loot, then you will not be giving the players any diamonds unless you hit on the 5000 gp diamond. However, it should be simple enough to swap in diamonds for some of lesser-value gems found in the gem hoards and caches. It is worth echoing here the introduction to the Dungeon Master's Guide:
The D&D rules help you and the other players have a good time, but the rules aren’t in charge. You’re the DM, and you are in charge of the game.
There is simply no rule which restricts the DM to only using the treasure hoard tables, so there is no sense in which even a strict rules-as-written approach to running the game should prevent you from just giving out some lower tier diamonds to your players. That said, treasure hoards are not the only canonical source of gemstones in the world.
You let them buy what they need at the market.
Gemstones are like large-denomination bills in the economy of D&D 5e:
Gems, Jewelry, and Art Objects
These items retain their full value in the marketplace, and you can either trade them in for coin or use them as currency for other transactions.
-Player's Handbook, "Selling Treasure"
Fortunately, as the Dungeon Master, you are not restricted to following the written guidance and rules to the letter, in fact, if you did, your world would be woefully incomplete. Gems are "trade goods" in the economy of D&D 5e, and any sufficiently large town or city is certain to have a shopkeeper that deals in precious gems. If a cleric needs a 300 gp diamond for revivify, they should typically be able to find one at the Waterdeep Zales outlet for 300 gp.