For Druid + Rogue at level 1; combat is not necessarily required.
Focusing on the rogue's DPR is, IMO, you as DM viewing this party through a very narrow lens. I suggest that, since (1) you only have two players, and (2) neither of them is from a warrior archetype, the adventures that you run for them until they get to second level should focus more on role play, exploration, and evasion / mobility and a bit less on melee combat. But when they do opt for melee combat, they need to try and engage on their own terms. (Credit: Sun Tzu's theory)
In-world, in a narrative sense, the odds that a Rogue and a Druid go and mix it up in the dark halls of a dungeon underground aren't very high. And, by crafting the adventures as suggested you get them working as a team from the get go.
Beyond that, they may not need a tank to create advantage.
How can the Druid help the Rogue get advantage?
Occasionally, with the Help action, but does the Druid player buy into that? Maybe and maybe not, but in any case that is between the two players to figure out. They need to work as a team because there are only two of them.
In some situations, Help will be a good use of an action, in others it will not. Let them figure that out by playing and by making decisions / choices.
Some Druid spells can offer advantage. Again, it is your players who need to work as a team to make the most of this.
Entangle (SRD p. 140)
Note that a creature that fails their save is
... restrained by the entangling plants until the spell ends.
From Appendix A, conditions, Restrained
Attack rolls against the creature have advantage, and the creature’s
attack rolls have disadvantage.
Rogue attack with advantage enables sneak attack.
Faerie Fire (SRD p. 141)
Any attack roll against an affected creature or object has advantage if the attacker can see it, and the affected cre ture or object can’t benefit from being invisible.
Rogue has advantage, Sneak attack.
From your comment:
My players have little experience overall and none with D&D 5e. It is their wish to start at level 1 in order to keep things simple.
It is OK to coach your players if they are new; you are the DM, coaching is a part of your role.
Change your DM'ing paradigm to fit your two-player party
Their first level of adventuring needs to empasize using their wits, not brawn, to accomplish their goals. Between the Druid's spells and the Rogue's ability to succeed on ability checks, and to Stealth around, and to occasionally apply a Sneak Attack if someone gets up into the Druid's grill, you can have some exciting and challenging adventures without a tank.
At level 2 Rogue gets cunning action, Druid gets wild shape; their options expand significantly.
Two of us played a two-rogue party for a session (urban setting) to help a DM get used to running a game. We used ranged attacks, movement, and anything but melee combat to achieve our aims. It's doable, it's fun, and it's still dangerous to the PC.