The landlord is requiring a 2 year lease, no pets, no smoking.

Landlords and Property Managers cannot treat emotional support animals as pets.

For example,  "NO PET" policies have different rules under ADA and the Fair Housing laws that mean you have to allow the animal because it's not considered a pet, but a necessity.  

I think I will do a refundable pet depsit and add a small pet fee to the rent each month.

That said, millennials ARE starting families and let's face it ~ when that happens, having extra space for kids/pets becomes more of a priority.

Same goes for pets, guests, outdoor equipment, etc.

I've had to do the same thing before with pets.  

Rentals are one area where the little guy can still compete with the mega corps and large apt complexes, often winning over some choice tenants with personal service, flexible terms, and small touches...Just a few ways, off the top of my head, that I think we can gain a competitive advantage over more rigidly run large complexes (though all markets vary, so these are based on my experiences)....) flexible terms (I offer a six month or one year lease; of course, most six month folks renew, but some like the flexibility; some large complexes are "one year or nothing" in my market..)) new mats (inside and out of the doors; bath, even runners or area rugs in high traffic area for vinyl plank flooring)...while they add some "wow factor" and look like gifts, there is self interest at work here, however, as the matting greatly reduces wear and tear on my flooring.) pets on approval ( I have some of the best behaved canine tenants imaginable, and their high quality tenant owners stay long term, are respectful, and pay well,yet are often shunned by many "no pets" larger places)) small (tax deductible) $20 gift card at holidays ..

.- Pet fees (@Brie Schmidt and others differentiate through renting to dog owners).

I would suggest you either prescreen people a bit over the phone before scheduling a showing time (asking questions about pets, income, and credit score eliminates 75% of the callers right there) and then confirming with them an hour or so before the showing (tell people if you can't reach them to confirm an hour before the showing time, the showing is cancelled), or, just publish a rental open house times like 7-9pm Wednesday night and 11-1pm Saturdays.