if you have to only move the tune voltage 1 volt, then you have to compromise. You need to resonate the tuning circuit (mostly very lightly couple it) so that a tiny change in capacitance makes a huge change in resonant frequency. For example, use a 100 nh inductance, and resonate it out with a 42 fF capacitance, or some other such relatively ludicrous thing. You will have poor loaded Q, and hence a lot of phase noise, but you will meet the tuning range.
Discrete VCOs use more like a 5 volt tuning range and a special varactor diode that has a big capacitance change over the 0 to 5 V range while having a good unloaded Q. THAT is how they get a big tuning range AND good oscillator noise.