2 momentary button into 1 persistence output with clk pulse
The following circuit might suit your purposes.



simulate this circuit &ndash; Schematic created using CircuitLab
R1 and R2 serve to pull down the inputs of latch1 when the temporary switches are open.
When one of the switches is closed, the first contact will cause latch one to latch that state. Further contact bounces will not alter the state of latch1.
If either of the buttons are pushed, the OR gate will give a positive output. This output will be both delayed and debounced by the RC circuit at it's output. The delayed and debounced signal is then buffered through an inverter.
Obviously, the logic can be modified in various ways while keeping the overall behavior the same. For example, the logic may be inverted, with the momentary switches bringing lines low rather than high.
To reduce IC count, a quad NAND gate IC  with Schmitt trigger inputs (such as the 4093B) could be used. Here is an example.



simulate this circuit