I'm not an expert in this field by any means (and my error message was different), but I spent last week trying to make Bitcoinj sign a transaction and send in raw form (i.e. without using transport protocol which Bitcoinj provides) and here's what I've learned (the hard way): You can't sign transactions like that. If you call tx.addSignedInput in a loop, you'll corrupt transaction's signature and it's gonna to be invalid. The solution (after brainstorming with my team and trying a few recipes here (this one didn't work), at Bitcoin Stack Exchange) was add all Inputs to the transaction and then sign them manually.

Transaction tx = new Transaction(networkParams);
tx.addOutput(Coin.valueOf(amount), targetAddress);
addInputsToTransaction(sourceAddress, tx, unspents, amount);
signInputsOfTransaction(sourceAddress, tx, key);

tx.verify();
tx.getConfidence().setSource(TransactionConfidence.Source.SELF);
tx.setPurpose(Transaction.Purpose.USER_PAYMENT);
String valueToSend = byteArrayToHexString(tx.bitcoinSerialize());

and the methods:

private void addInputsToTransaction(Address sourceAddress, Transaction tx, @NonNull BalanceResponse.Unspents[] unspents, Long amount) {
    long gatheredAmount = 0L;
    long requiredAmount = amount + TX_FEE;
    for (BalanceResponse.Unspents unspent : unspents) {
        gatheredAmount += unspent.getAmount();
        TransactionOutPoint outPoint = new TransactionOutPoint(networkParams, unspent.getvOut(), Sha256Hash.wrap(unspent.getTxId()));
        TransactionInput transactionInput = new TransactionInput(networkParams, tx, hexStringToByteArray(unspent.getScriptPubKey()),
                outPoint, Coin.valueOf(unspent.getAmount());
        tx.addInput(transactionInput);

        if (gatheredAmount >= requiredAmount) {
            break;
        }
    }
    if (gatheredAmount > requiredAmount) {
        //return change to sender, in real life it should use different address
        tx.addOutput(Coin.valueOf((gatheredAmount - requiredAmount)), sourceAddress);
    }
}

private void signInputsOfTransaction(Address sourceAddress, @NonNull Transaction tx, ECKey key) {
    for (int i = 0; i < tx.getInputs().size(); i++) {
        Script scriptPubKey = ScriptBuilder.createOutputScript(sourceAddress);
        Sha256Hash hash = tx.hashForSignature(i, scriptPubKey, Transaction.SigHash.ALL, true);
        ECKey.ECDSASignature ecdsaSignature = key.sign(hash);
        TransactionSignature txSignature = new TransactionSignature(ecdsaSignature, Transaction.SigHash.ALL, true);

        if (ScriptPattern.isP2PK(scriptPubKey)) {
            tx.getInput(i).setScriptSig(ScriptBuilder.createInputScript(txSignature));
        } else {
            if (!ScriptPattern.isP2PKH(scriptPubKey)) {
                throw new ScriptException(ScriptError.SCRIPT_ERR_UNKNOWN_ERROR, "Unable to sign this scrptPubKey: " + scriptPubKey);
            }
            tx.getInput(i).setScriptSig(ScriptBuilder.createInputScript(txSignature, key));
        }
    }
}

I hope, it will help you.