The thread title is quite misleading. It ought to read "New German bomber", not "New axis bomber".
The three listed German bombers are undoubtedly the leading candidates for a new Axis bomber from Germany. Lets also put the leading options from Italy and Japan into the mix to make the thread about a new Axis bomber.
SM.79-II:Crew: 6 (pilot, co-pilot, flight engineer/gunner, radio operator, bombardier, rear gunner)
Length: 16.2 m (53 ft 2 in)
Wingspan: 20.2 m (66 ft 3 in)
Height: 4.1 m (13 ft 6 in)
Wing area: 61.7 m² (664 ft²)
Empty weight: 7,700 kg (16,975 lb)
Loaded weight: 10,050 kg (25,132 lb)
Powerplant: 3 × Alfa Romeo 128-RC18 radial engines, 642 kW (860 hp) each
Maximum speed: 460 km/h (286 mph) at 3,790 m (12,450 ft)
Range: 2,600 km (1,615 mi)
Service ceiling: 7,500 m (24,600 ft)
Rate of climb: 5.3 m/s (1,050 ft/min)
Wing loading: 165 kg/m² (33.8 lb/ft²)
Power/mass: 0.173 kW/kg (0.106 hp/lb)
Guns:
2 × 12.7 mm (0.5 in) Breda-SAFAT machine gun
2 × 7.7 mm (0.303 in) machine guns in lateral "waist-gun" ports (optional)
Bombs:
1,200 kg (2,645 lb) internal bomb load or two external 450 millimetres (17.72 in) torpedoes
SM.82Crew: 4
Capacity: 40 troops
Length: 22.9 m (75 ft 1½ in)
Wingspan: 29.68 m (97 ft 4½ in)
Height: 6.0 m (19 ft 8.25 in)
Wing area: 118.6 m² (1,276.64 ft²)
Empty weight: 10,550 kg (bomber 11,200 kg) (23,259 lb)
Max. takeoff weight: 18,020 kg (bomber 18,410 kg) (39,727 lb)
Powerplant: 3 × Alfa Romeo 128 RC.21 9-cylinder radial engines, 708 kW (950 hp) each
Maximum speed: 347 km/h (187 kn, 212 mph)
Cruise speed: 250 km/h (135 kn, 125 mph) at 3,000 m (9,840 ft)
Stall speed: 110 km/h (59 kn, 68 mph)
Range: 2,100 km (1,134 nmi, 1,864 mi)
Service ceiling: 6,000 m (19,685 ft)
Guns:
1 × 12.7 mm (.5 in) Scotti machine gun in dorsal turret
3 × 7.7 mm (.303 in) Breda-SAFAT machine guns in ventral and lateral positions
Bombs:
4,000 kg (8,818 lb) bombload
Cant Z.1007Crew: 5
Length: 18.35 m (60 ft 2.5 in)
Wingspan: 24.80 m (81 ft 4.5 in)
Height: 5.22 m (17 ft 1.5 in)
Wing area: 70 m² (750 ft²)
Empty weight: 9,396 kg (20,715 lb)
Max. takeoff weight: 13,621 kg (30,029 lb)
Powerplant: 3 × Piaggio P.XI RC.40 radial engines, 745 kW (1,000 hp) each
Maximum speed: 458 km/h (245 kn, 285 mph)
Cruise speed: 338 km/h (183 kn, 210 mph)
Range: 1,795 km (969 nmi, 1,115 mi)
Service ceiling: 7,500 m (25,000 ft)
Guns:
2 × 12.7 mm (0.5 in) Isotta-Fraschini Scotti or Breda-SAFAT machine guns
2 × 7.7 mm (0.303 in) Breda-SAFAT machine guns
Bombs:
1,200 kg (2,645 lb) of bombs internally. 1,000 kg (2,200 lb) externally on underwing hardpoints. Or a combined load of 2,200 kg (4,900 lb) of bombs internally and on external hardpoints.
2 × 450 mm (17.7 in) 800 kg (1,800 lb), torpedoes
Ki-21-II 'Sally'Crew: 5-7
Length: 16.0 m (52 ft 6 in)
Wingspan: 22.50 m (73 ft 10 in)
Height: 4.85 m (15 ft 11 in)
Wing area: 69.90 m² (752.12 ft²)
Empty weight: 6,070 kg (13,354 lb)
Loaded weight: 10,600 kg (23,320 lb)
Powerplant: 2 × Mitsubishi Army Type 100 (Ha-101)(Mitsubishi Kasei) 14 cylinder radial engine, 1,119 kW (1,500 hp) each
Propellers: three-blade metal variable-pitch propellers propeller
Maximum speed: 485 km/h (301 mph) at 4,700 m (15,400 ft)
Cruise speed: 380 km/h (236 mph)
Range: 2,700 km (1,680 mi)
Service ceiling: 10,000 m (32,800 ft)
Rate of climb: 13 min 13 sec to 6,000 m (19,680 ft)
Guns:
4× 7.7 mm (.303 in) flexible Type 89 machine guns in nose, ventral, beam and tail positions
1× 12.7 mm (.50 in) Type 1 Machine Gun in dorsal turret
Bombs:
1,000 kg (2,200 lb) of bombs
P1Y1 Ginga 'Frances'Crew: 3
Length: 15.00 m (49 ft 2⅜ in)
Wingspan: 20.00 m (65 ft 7¼ in)
Height: 4.30 m (14 ft 1¼ in)
Wing area: 55 m² (592 ft²)
Empty weight: 7,265 kg (16,020 lb)
Loaded weight: 10,500 kg (23,149 lb)
Max. takeoff weight: 13,500 kg (29,762 lb)
Powerplant: 2 × Nakajima NK9C Homare 12 18-cylinder radial engines, 1,361 kW (1,825 hp) (take-off) each
Maximum speed: 547 km/h (295 knot, 340 mph) at 5,900 m (19,400 ft)
Cruise speed: 370 km/h (200 knots, 230 mph) at 4,000 m (13,125 ft)
Range: 5,370 km (2,900 nmi, 3,337 mi)
Service ceiling: 9,400 m (30,840 ft)
Wing loading: 191 kg/m² (39.1 lb/ft²)
Power/mass: 0.20 kW/kg (0.16 hp/lb)
Guns:
1× flexible, nose-mounted 20 mm Type 99 cannon
1× flexible rear-firing 13 mm Type 2 machine gun
Bombs:
up to 1,000 kg (2,205 lb) of bombs or 1× 800 kg (1,800 lb) torpedo
H8K2 'Emily'Crew: 10
Length: 28.15 m (92 ft 4 in)
Wingspan: 38.00 m (124 ft 8 in)
Height: 9.15 m (30 ft)
Wing area: 160 m² (1,721 ft²)
Empty weight: 18,380 kg (40,436 lb)
Loaded weight: 24,500 kg (53,900 lb)
Max. takeoff weight: 32,500 kg (71,500 lb)
Powerplant: 4 × Mitsubishi Kasei 22 radial engines, 1,380 kW (1,850 hp) each
Maximum speed: 465 km/h (290 mph)
Range: 7,150 km (4,440 mi)
Service ceiling: 8,760 m (28,740 ft)
Rate of climb: 8.1 m/s (1,600 ft/min)
Wing loading: 153 kg/m² (31 lb/ft²)
Power/mass: 0.22 kW/kg (0.14 hp/lb
Guns:
5× 20 mm Type 99 cannon (one each in bow, dorsal, and tail turrets, plus one each in two waist blisters)
5× 7.7 mm (.303 in) Type 92 machine guns in fuselage hatches
Bombs:
2× 800 kg (1,764 lb) torpedoes or 2,000 kg (4,410 lb) of bombs or depth charges
There we go, nine prospective Axis bombers. Do217E, H8K2, He177A-5, Ju188A-1, Ki-21-II, P1Y1, SM.79-II, SM.82 and Z.1007.