Then just allocate between the two based on their relative attractiveness.
It shouldn't be too hard to come up with a relatively sane formula.
If the anticipated real return from the bonds is negative, don't buy any!
I don't think I'd bother at a real expected return of less than 1-2%.
Unlike "fixed ratio" rebalancing schemes, the results from this approach are not particularly dependent on how often you do it.

This is better than using a fixed ratio, if the goal is to improve the return one what you get from having the fixed stocks / bond ratio. Substitute 'bond' with 'cash' or 'TIPS' which doesn't change the goals much. To keep it simple, you can use an allocation such as (100 - CAPE)% stocks, (CAPE)% bonds. This gives a higher bond allocation when the CAPE ratio is high, and a lower exposure to bonds when CAPE is very low (stocks cheap). But it always gives at least some small bond exposure. Historically 5 < CAPE < 40.

However, if the goal is to outperform what you would get over the long-term with a fixed 100% stock allocation, then any bond allocation strategy - even if moving in and out strategically - is far more difficult than most investor realise. Excuse me for re-quoting, but it is the central idea:
The gains you make on adding capital at pessimistic periods has to counteract far larger effect of having a reduced exposure for the bulk of your holding period. To put this another way, even if you beat the market with your low entry points (the timing itself is successful and market-beating) then this is not a sufficient condition to beat the market as a whole with your entire portfolio. You have to not only have market beating returns for the extra stock purchases at market lows, but that outperformance needs to exceed the underperformance from the huge drag owing to the reduced equity exposure over most of the portfolio's life.

If on average you the programme I describe above has you invested with 20% bonds, 80% stocks (it varies, but that is what you have on average), then the dynamic mix above will outperform the fix 20/80 mix. However both strategies will still underperform the 100% stocks / 0% bonds mix over multi-decade stretches.

If you get fancy, you could have the stock exposure ranging between 0% and 100% in association with the historical range of CAPE ratios. You would then use (100/35*(CAPE-5))% bonds, (100 - 100/35*(CAPE-5))% stocks. That might be worth backtesting with the spreedsheet data provided at Robert Shiller's home page.

- Manlobbi