At this stage of the beekeeping season, when a hive becomes queenless, the best thing to do is to combine it with another colony.
1. Put a couple sheets of newsprint over the brood boxes of a strong/healthy colony.
2. Cut several two-inch slits in the paper.
3. Place the brood boxes of the queenless colony on top of the newsprint.
4. Put a couple medium honey supers on top of the queenless brood boxes.
5. Place inner and outer lids on top of the medium honey supers.
It takes the bees a couple days to eat through the paper. This method works because it allows the bees to be combined gradually rather than throwing two colonies together suddenly.
It is better to make use of all of the foragers from the queenless hive rather than letting them slowly die out. Why not put their amazing skills to work and make one strong colony with a higher population?