In my experience, a crew of 6 or 7 men can replace as many as 125 ties a day, if they have the right equipment and preparation. There are narrow gauge tie replacers available, as well as tie cranes and tampers. I know the C&TS has a tamper from the South Buffalo RR, though I don't know about a tie crane or tie replacer. And using an air spiker is almost as much work as spiking by hand.
As for the number of ties required, based on two-foot centers, there are about 2,640 ties per mile. The average life of a tie is about 35 years, so at that rate of attrition, you have to replace 75 ties a mile per year just to keep up. Since we know for sure that not all 2,640 ties are going to fail at once, it's probably a safe bet to plan on replacing 100 ties per mile annually.
Even at that, that's 6,400 ties per year or about 51 days of work just to replace the ties. That doesn't count switch timber, yard tracks or anything else. That also doesn't allow for travel time to and from the job site, the time to pick up the old ties or lay out the new ones or the time lost clearing up for trains. By the time all those things are factored in, putting in 6,400 ties annually will probably take at least 60 days or 12 weeks, if you can work five days a week.
Based on the current cost of ties, spikes, fuel and labor, it's probably going to cost about $60-$70 per tie installed, or $400,000 per annum from this time forward. Remember, this is only for ties, not ballast, surfacing or anything else. It costs a lot of money to maintain a railroad.