You have a few options, two of which in particular come to mine.
Many times, when a Vendor says "no NAT is allowed", they really mean "no PAT is allowed". This is typically because of a PAT being, by definition, unidirectional. In most VPN type systems, both peers need to be able to initiate traffic to the other, which isn't possible in a unidirectional communication system, like PAT.
As such, the solution is to give your Checkpoint Firewall a Private address, say 192.168.1.25. Then create a Static NAT on your ASA to translate 192.168.1.25 to one of the IPs in the additional /30 your ISP has assigned.
From the VPN configuration perspective, the remote end will use the Public /30 address as their "opposing peer", and you will use the other end's IP address as your "opposing peer". Then, as long as NAT Traversal is enabled (which it typically is by default, but I can only confirm that on the Cisco ASA), the VPN tunnel should be able to build through the Static NAT.
This is your ideal solution, I would suggest going this route if you can. Mainly, because you are holding in reserve the other 3 IPs of the 4 they gave you in the /30. But, if you see no use for these, now or in the future, Solution 2 might work out for you:
Use the /30 assigned by your ISP as its own "transit" network between the ASA and Checkpoint. You'll need an additional interface on the ASA, or you could have the same effect with a Trunk configuration. The ASA will have two segments off it, the transit network, and the DMZ network. Then your "inside" network will simply be "behind" the Checkpoint.
I was going to try to explain this with text, but I figured a picture was easier. I made up the IPs, since you didn't provide them:
You could either use Identity NAT on the ASA to allow the traffic through un-natted, or simply configure a NAT Exemption for the /30 network.
All other options beyond this require a bit of creativity, but are probably considered non-standard, and as such should be avoided unless the solutions above don't work. If they don't, please provide specific details as to why, so we can try to provide additional solutions.