You could use two monostables (aka one-shots). It depends what you want to set, and what will be changing.
Inserting a fixed-duration monostable between each output and each MOSFET gate will give you a fixed ON-time. If the 4047's frequency is fixed, this corresponds to a fixed duty cycle. If the 4047's frequency is variable, the duty cycle will be higher at higher frequencies, because the ON-time is fixed.
Inserting a fixed-duration delay between each output and each MOSFET will give you a fixed OFF-time (within each half cycle). If the 4047's frequency is fixed, this also corresponds to a fixed duty cycle. If the 4047's frequency is variable, the duty cycle will be lower at higher frequencies.
If you want to set the duty cycle to a constant value regardless of frequency, things get more complicated. You could use a different kind of oscillator that generates a sinewave and pass that through some comparators, or if you want a simple duty cycle like 25% for each MOSFET, you can run the oscillator at a multiple of the main frequency and use a frequency divider to divide the cycle into pieces.
The 4047 seems convenient because it has complementary outputs, but that's the only advantage it has over other methods, because it saves you one inverter IC. That advantage becomes less important if you add monostables to those outputs. And you should already be using a MOSFET driver to ensure quick switching - the 4047's outputs can only source and sink a few mA. So I think you could reconsider your timing source.
For example an oscillator based on a 32000 Hz watch crystal will give you a nice stable frequency that you can divide down by varying amounts. You could also use a small microcontroller, with a watch crystal for its second oscillator, to generate both control signals. The microcontroller could monitor the output voltage using an analogue input, and adjust the duty cycle accordingly. This could be a good next step in the development of your inverter.