In a private chain of one-hundred miners where we assume all miners have comparable computing power to mine with is there any way to guarantee each miner mines an approximately equal number of blocks per day?
Miners agree to use their computational resources to run the blockchain. In return, they get a chance to earn some Ether in doing this. Any time a transaction is mined, the miners compete to "win" this transaction.
In your scenario, all the miners have the same computing power, so unless the difficulty function increases for succeeding transactions, they should take similar time to mine any transaction on the blockchain.
In a proof of work chain it is not possible to guarantee a miner will mine at least one block per day since finding a block is close a random event.
Assuming that N participants are in similar conditions the probability of finding one block at any time is 1/N (and the probability of not finding one is 1 - 1/N).
If in one day there k blocks then the probability of finding at least 1 is
1 - (1 - 1/N)^k.
If you have N=100 miners and the chain generates one block per minute k=1440 then the probability of mining at least 1 block is 0.9999994815818231. A miner is really really unfortunate if it can't mine at least one block per day.