Your're correct that there's no way to have a constructor run with contracts defined in the genesis.json. Though there is a way to set state in the contract at genesis time, and that's by using the storage
parameter, similar to the code
parameter. See the below sample, taken from this question.
{
"alloc": {
"0x0000000000000000000000000000000000000020": {
"code": "606060405236156100c45760e060020a60003504631290948581146100...<truncated>...",
"storage": {
"0x0000000000000000000000000000000000000000000000000000000000000001": "0x02",
"0x0000000000000000000000000000000000000000000000000000000000000002": "0x04",
"0x29ecdbdf95c7f6ceec92d6150c697aa14abeb0f8595dd58d808842ea237d8494": "0x01",
"0x6aa118c6537572d8b515a9f9154be55a3377a8de7991cd23bf6e5ceb368688e3": "0x01",
...
}
},
"0xed9d02e382b34818e88b88a309c7fe71e65f419d": {
"balance": "1000000000000000000000000000"
},
"0xca843569e3427144cead5e4d5999a3d0ccf92b8e": {
"balance": "1000000000000000000000000000"
},
"0x0fbdc686b912d7722dc86510934589e0aaf3b55a": {
"balance": "1000000000000000000000000000"
},
...
}
},
"coinbase": "0x0000000000000000000000000000000000000000",
"config": {
"homesteadBlock": 0
},
"difficulty": "0x0",
"extraData": "0x",
"gasLimit": "0x2FEFD800",
"mixhash": "0x00000000000000000000000000000000000000647572616c65787365646c6578",
"nonce": "0x0",
"parentHash": "0x0000000000000000000000000000000000000000000000000000000000000000",
"timestamp": "0x00"
}
The storage section allows you to set the state at indivudual storage slots in the contract. The difficulty of course is knowing which ones to set to what, but you can figure that out by examining either the constructor bytecode or by deploying your contract on a testnet and examining the storage slots the constructor allocates.