I do not fully understand your problem but it sounds like:
You have a 29 volt solidstate relay that controlls something
You bought a mecahnical relay, with a coil, that is specified at 24 volts.
When you energize the relay, it does not fully close.
It sounds like your problem is either:
1) you bought a 24v AC relay, and are maybe giving it 24v DC. Maybe the rectifier circuit above will solve that
2) The source of the 29v is not capable of driving the current draw of the 24V relay, so when it is energized, the 29 volts drops to something much lower...maybe 12 volts, and that is not enough to hold the relay contacts closed. In that case, you simply have the wrong type of coil relay, you need more turns of wire on the coil. Measure the actual voltage across the relay coil when it is trying to close, and tell us what you read.