In my immediately previous career I was a bankruptcy attorney. I either put companies into a Chapter 7 (closed the business) or into a Chapter 11 (court restructuring). I've seen, both from the ones I've done and the ones I've watched, probably hundreds if not thousands of companies declare bankruptcy, or more importantly not be able to afford bankruptcy and their owners declare bankruptcy. Based on that experience, there are two industries that I will never be a part of (as an owner or investor, in any way shape or form): restaurants and daycare centers.
The three (from what I've seen) industries that take the biggest hit from an economic downturn that aren't able to survive it are the restaurant industry, the daycare industry, and the construction industry. But when times are good, the construction industry can make enough profit to justify the risk. Plus they are able to cut back (to almost nothing) on their expenses to weather economic downturns. The same can't be said of either the restaurant industry or the daycare industry. They are required to maintain high overhead despite the low income. Which requires large cash reserves (or lines of credit) for "just in case" situations.
Moving specifically to the daycare industry, on paper they always look like the print money. And I write a weekly check to my daycare, so I'm well aware of how both sides of the equation operate. But all that glitters isn't gold. Most daycares have a substantial amount of administrative work and expenses, specifically as it relates to the licensing requirements and the insurance requirements. Those two have a tendency of sucking up most of the free cash (assuming it wasn't gone already for franchise fees). Employees are hourly, and you often have to manage them intensely. If one calls out sick, you need to be able to have a back up on the spot to maintain ratios for insurance and licensing needs. That back up will, in one way or another, cost you. Employees aren't easily found either. They typically aren't paid much, but have to withstand rigorous background checks. Finding replacements are hard, and there is typically high turnover. In my experience, most daycares service the middle to lower class (as the upper class can afford, and often find it cheaper to afford a private nanny, than to pay for daycare for 2 or 3 kids). Nothing against middle and lower class working people, but sometimes employment ends for them somewhat randomly, or a big financial emergency hits that they can't afford. Contracts for long term services are difficult, if not impossible, to enforce. Chasing parents for bounced checks can often become a job in and of itself. That's not to speak of the food subsidy requirements, the food preparation and associated expenses (or the nutritionist you need to hire), the registered nurse you need to have on call in the event of an issue, and the myriad of other heath and safety requirements. That doesn't even get into the basic rent, utilities, supplies (art, books, cleaning, furniture), ect. expenses.
That's also looking past the potential for "inflated numbers" that the old owner may have. If it's really printing money, why is the old owner "motivated to sell because of a divorce." There are many reasons that may make it valid, but it causes some suspicion. If you do want to move forward, have as much of it owner financed as you can, and have the transfer littered with representations and warranties that you can go after them in the event the business isn't as he said it is.
In the end, I wouldn't touch the industry. But your association of risk may be different.