Outside condensers whether AC or HP have certified ratings by AHRI. These ratings are both BTUs and efficiency. Sounds from your post that you may be undersized. Unfortunately you can not increase your BTUs. Short of getting a new and correctly sized system, you might look at your ductwork system including return air along with possible insulation improvements.

IMO

How long is very, very long? Do you have a set-back thermostat and do you know how to use it? Are you home and away on a predictable schedule?

Much easier to reduce infiltration and increase insulation as has been said. You might change out the skylight glass to low-e if it isn't already.

I imagine such a drastic change involved a manual J which most certainly took the skylights into consideration.

The skylights can be tinted which will make a sizeable difference. I had a half circle window tinted by a company that does auto tinting and it was very reasonable and made a huge difference. I would also check for duct leakage and correct any with mastic tape or brush on mastic. I am sure with some focus on sealing and insulating that the system would handle the load much better.

Yes, I have a programmable thermostat and know how to use it. As far as how long is long...for instance today at 23opm the thermostat was set for 72 and the house temp was 77. it didn't drop to 76 'til 630pm when the weather changed over to stormy weather. i have been keeping window shades down, and curtains pulled over sliding glass doors. i don't know how much it helps.
i am considering getting shades for the 2 skylights, and possibly a ceiling fan for that room.
as far as a Manual J - i had 5 estimates and not one did it. said the space was small and could assess without. i found one independent company who would do it, but wanted nearly $700, which seemed outrageous.
i should have written in my initial post that the original 5 ton unit we had was in place to cool the whole house. we eventually put in a 2nd zone to handle the bedrooms only - that is a 2.5 ton unit. so, when it came to replacing the original 5 ton unit - i knew that a smaller unit would be recommended, as it no longer was connected to the bedroom side of the house.
At this point, i'm going to contact the installer and have him look at the ductwork for leaks.

I see - the second zone made 3 tons seem reasonable. Shading the skylights should really help but shade them from the outside.

As far as you temp changes - 2:30-6:30 is usually the highest heat load. A properly sized a/c would not be able to cool during this time on a design temp day (ie a day like most of the country is having this week). A properly sized system can MAINTAIN temperature on a day that is in the 95%ile for temperature in the area- often around 95 degrees. While winter varies considerably in the country, most places peak around 100 and get in the 90s with some regularity in the summer (obviously SW deserts and places with elevation are different).

So it really maybe a problem of not knowing how to use your programmable stat or unrealistic expectations (or it maybe just an undersized unit). I generally would not be asking an a/c system to reduce the temp of the house in the afternoon. I'm not sure you get much benefit at all from setbacks in an a/c environment. What kind of setbacks are you doing? Where do you live and how hot has it been?

I always like to point out that manual J's are code around here (NC) so when contractor's don't want to do it, I am amazed. That being said - they are often done wrong or ignored.

Thanks so much for your reply. When you suggest shading from the outside, are you referring to removable skylight covers that i've seen online? Or, will tinting from the outside help? what about the products from 3M?

Regarding the programmable thermostat, I have been manually handling the thermostat since the beginning of the week. I'm up at approx 6:45am, and the therm reads 73. I lower it to 71 or 72, because I want it at the cooled level before the day starts to heat up. This way the unit just needs to maintain, as you said. It cools down easily, but by 11:00/11:30 it starts creeping up and that's it for daylight hours. It won't bring the temp down.
We live in northern NJ, and we had a day in the 90's yesterday. It will be in the 80's today. I'm worried that once we have a string of days in the 90's, the house is just not going to cool off.

I know it's not ideal, because everyone's house is different, but those I checked in with yesterday had homes that managed to stay cooled in the 70-72 degree area. Like I said this is a Trane unit, installed a year ago with new air handler and ductwork (we had to switch everything over from freon). Should be working better.

Tinting is fine. Velux has an outside mounted shading system I believe. Just know that if you put the shades on the inside, that much of the heat still makes it in.

I would venture to say that getting a house in northern NJ to 70 degrees yesterday was beyond the expected design conditions. Maybe what you want but is not what systems are designed to do. The inside design temp around here is 75 degrees so that systems are designed to get to 75 on a really hot day.

That being said - you want it cooler. But what you are asking is not really what you can expect a system to do. Based on what you have said, it is my guess that your system is fine (I absolutely could be wrong). If you tint the skylights, you will probably tilt the scales to your favor.

Question - what is your humidity? My only thought is that maybe 75 and dry may be fine for you. Don't necessarily get caught up in the temperature. I've gotten very used to 76 in our new house because it is so dry - I think I set at 73 in the last house. My wife often won't let me turn the ceiling fan on because she is too cold.

Most of your neighbors probably have oversized equipment which is why they are able to get to 70 degrees.

I don't have a humidistat so can't say what the humidity is. It's not common to have that here.

But, the air is feeling stale and that's not a good thing. You can smell the staleness when you enter the house.

My skylights are Velux, so i'm going to check into that. And, also putting up a ceiling fan in our family room. Very frustrating - i've been in the house for 16 years and didn't have to do either. Now, after spending a great deal on a new system, I have to do all this, too. Again, thanks.