I've got two designs for Assault Transports, one the size of a standard Destroyers (30,000 tons) and one the size of a cruiser (100,000 tons).
Big Transport
The bigger transport can carry a full brigade and all its support companies and comes with a full defense suite of AMMs and Gauss PD as well as 10,000 tons of Hangar capacity to store Ground Attack Fighters to support the troops. It is meant to act as an invasion mothership, able to launch small invasions by itself without any support from Auxiliary Carriers or the like.
Big Transport class Assault Transport 100,000 tons 1,635 Crew 13,945 BP TCS 2,000 TH 10,000 EM 0
5000 km/s Armour 10-191 Shields 0-0 HTK 391 Sensors 18/18/0/0 DCR 130 PPV 138
Maint Life 1.29 Years MSP 14,715 AFR 800% IFR 11.1% 1YR 9,257 5YR 138,859 Max Repair 5000 MSP
Hangar Deck Capacity 10,000 tons Troop Capacity 25,000 tons Drop Capable Magazine 1,020
Line Captain Control Rating 4 BRG AUX ENG PFC
Intended Deployment Time: 12 months Flight Crew Berths 200 Morale Check Required
20000M 125% (1) Power 10000 Fuel Use 11.05% Signature 10000 Explosion 12%
Fuel Capacity 12,007,000 Litres Range 195.6 billion km (452 days at full power)
Quad Gauss Cannon 25.00 Turret (12x20) Range 50,000km TS: 25000 km/s Power 0-0 RM 50,000 km ROF 5
Gauss PD Fire Control (4) Max Range: 57,600 km TS: 25,000 km/s 83 65 48 31 13 0 0 0 0 0
Size 1 Missile Launcher (80) Missile Size: 1 Rate of Fire 25
AMM Fire Control (4) Range 28.7m km Resolution 1
Small Point-Defense Active Sensor Suite (1) GPS 36 Range 14.4m km MCR 1.3m km Resolution 1
Milspec EM Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Milspec Thermal Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Compact ECCM-3 (8) ECM 40
This design is classed as a Military Vessel for maintenance purposes
Small Transport
The second smaller transport though is, admittedly, my favored of the two. While it sacrifices AMMs and most of the troop capacity of its bigger sister, it is faster and has a lower profile as a result of its smaller engine and size. I even consider the ability to only carry 1 Battalion at a time to have a silver lining; if a ship gets killed its far less of a big deal losing 1 instead of 5. However cost wise the bigger transport is more efficient at carrying troops.
Small Transport class Assault Transport 30,000 tons 568 Crew 5,416.1 BP TCS 600 TH 5,000 EM 0
8333 km/s Armour 10-86 Shields 0-0 HTK 135 Sensors 18/18/0/0 DCR 60 PPV 60
Maint Life 1.23 Years MSP 3,385 AFR 240% IFR 3.3% 1YR 2,333 5YR 34,989 Max Repair 2500 MSP
Troop Capacity 5,000 tons Drop Capable
Line Captain Control Rating 3 BRG AUX ENG
Intended Deployment Time: 12 months Morale Check Required
10000M 125% (1) Power 5000 Fuel Use 15.62% Signature 5000 Explosion 12%
Fuel Capacity 4,408,000 Litres Range 169.3 billion km (235 days at full power)
Quad Gauss Cannon 25.00 Turret (8x20) Range 50,000km TS: 25000 km/s Power 0-0 RM 50,000 km ROF 5
Gauss PD Fire Control (2) Max Range: 57,600 km TS: 25,000 km/s 83 65 48 31 13 0 0 0 0 0
Small Point-Defense Active Sensor Suite (1) GPS 36 Range 14.4m km MCR 1.3m km Resolution 1
Milspec EM Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Milspec Thermal Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Compact ECCM-3 (2) ECM 40
This design is classed as a Military Vessel for maintenance purposes
Small Transport class Assault Transport 30,000 tons 568 Crew 5,416.1 BP TCS 600 TH 5,000 EM 0
8333 km/s Armour 10-86 Shields 0-0 HTK 135 Sensors 18/18/0/0 DCR 60 PPV 60
Maint Life 1.23 Years MSP 3,385 AFR 240% IFR 3.3% 1YR 2,333 5YR 34,989 Max Repair 2500 MSP
Troop Capacity 5,000 tons Drop Capable
Line Captain Control Rating 3 BRG AUX ENG
Intended Deployment Time: 12 months Morale Check Required
10000M 125% (1) Power 5000 Fuel Use 15.62% Signature 5000 Explosion 12%
Fuel Capacity 4,408,000 Litres Range 169.3 billion km (235 days at full power)
Quad Gauss Cannon 25.00 Turret (8x20) Range 50,000km TS: 25000 km/s Power 0-0 RM 50,000 km ROF 5
Gauss PD Fire Control (2) Max Range: 57,600 km TS: 25,000 km/s 83 65 48 31 13 0 0 0 0 0
Small Point-Defense Active Sensor Suite (1) GPS 36 Range 14.4m km MCR 1.3m km Resolution 1
Milspec EM Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Milspec Thermal Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Compact ECCM-3 (2) ECM 40
This design is classed as a Military Vessel for maintenance purposes
EDIT: I think I might have overdesigns these ships somewhat to be honest. Far too much emphasis on protection, speed and range at the cost of pure transport capability which is what these ships are meant to be. Still, its nice being able to send an assault force from your capital to the enemy planet in one go and be confident they will get there in one piece and without stopping. Here is a more 'pure' transport using CIWIS and Commercial Engines to save a lot of space, allowing me to double the amount of transport bays for the Big Transport.
Pure Transport
Pure Transport class Assault Transport 99,998 tons 1,131 Crew 7,444.7 BP TCS 2,000 TH 4,000 EM 0
2000 km/s Armour 10-191 Shields 0-0 HTK 326 Sensors 18/18/0/0 DCR 129 PPV 0
Maint Life 1.32 Years MSP 4,606 AFR 808% IFR 11.2% 1YR 2,792 5YR 41,878 Max Repair 1000 MSP
Troop Capacity 50,000 tons Drop Capable
Line Captain Control Rating 3 BRG AUX ENG
Intended Deployment Time: 12 months Morale Check Required
20000C (1) Power 4000 Fuel Use 1.12% Signature 4000 Explosion 5%
Fuel Capacity 1,000,000 Litres Range 161 billion km (931 days at full power)
CIWS-250 (12x10) Range 1000 km TS: 25,000 km/s ROF 5
Milspec EM Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
Milspec Thermal Sensor Suite (1) Sensitivity 18 Detect Sig Strength 1000: 33.5m km
ECM 40
This design is classed as a Military Vessel for maintenance purposes