The second D-Link will only function as a router. :(
I would probably recommend you trying to get something that supports external antennas. This would allow you to fine tune your connection. Otherwise, try to re-locate the wireless router to a location that better serves your needs.
Not really understanding why you went with a second Router/AP instead of just an additional AP (?). Unless, of course, it was because of price. Funny how Routers/AP's are now priced less than just stand-alone AP's. I guess the manufacturers are doing this since they know Router/AP's are usually the piece of hardware folks get and they want to get them "branded". (?)
Sounds like what you are looking for is a "Range Extender (Repeater)". Might be less hassle with that particular router (DI-624) to get a stand-alone "Range Extender (Repeater)" versus a full-blown AP that supports "Repeater Mode" as, from quick glance at DI-624 specs, it doesn't seem to have WDS. I'm also using D-Link and ran into that problem after trying to extend my wireless. I'm using an older DI-764 (802.11a+, 802.11b+) router (works great!) and picked up a DWL-7100AP (802.11a+, 802.11g/b+) thinking I could use the "Repeater Modes". Lack of WDS on the DI-764 resulted in my purchasing a second DWL-7100AP. (One connected directly to router and other repeating.) Not exactly the most cost effective "range extending" solution, but I now have 802.11g in the loop -- which is being used by a Media Center.
Anyway, a quick glance at the DI-624 specs is leaving me to believe that you might find yourself in a similiar situation if getting a "full blown AP capable of Repeater Mode". Quickly looking at several of them on D-Link's website, they are saying "Not Compatible with DI-624".
A "stand alone repeater" should work just fine. Check out the DWL-G800AP:
The DWL-G800AP is stated to be compatible with the "DI-624 (revC) 2.37 and higher". I have two very similiar D-Link products like the DWL-G800AP. One is a a wireless-ethernet bridge and the other is an 802.11b "Range Extender". They are in the same type of casing -- the little box. These guys are easy to setup and then just thrown on a desk and forgotten. Completely seamless. Keep in mind that going through any repeater, you'll get some of a throughput loss. The DWL-G800AP states it's max throughput is
54 Mbs and I'm assuming that the DI-624 goes up to 108 Mbs (in theory). My DI-764, in theory, can push 108/22 (802.11a, 802.11b) and the DWL-7100AP can push 108/108 (802.11a, 802.11g) but in "Repeater Mode" found the best compromise to be so-called 54 Mbs. In real use, I found the actual throughput drop to be neglible with 54 Mbs compared to 108 Mbs. This is based upon moving files around the WLAN, not internet (which cable modem is bottleneck anyway). The numbers are more marketing than anything else, unless you happen in live in prestine RF-clean lab conditions. :^)
Oh, by the way, if you do decide on a DWL-G800AP, I believe E-Cost has them.
I purchased the two little D-Link guys (bridge/repeater) off Ecost, as I found them to be the least expensive. Free shipping (or overnight for only $10) as well. Not affilliated with them or anything, but can say that you will get your product extremely quickly for less. Now, if you ever need to do a return with them, thats another matter. (They are horrible in that regard.)
Looks like I shot from the hip a little there. I went back and looked at the DWL-2100AP and read in the Knowledge Base that it is, in fact, capable of repeating the DI-624.
Guess you'll want to compare the price versus featuers of the DWL-2100AP versus, say, the stand-alone guy (DWL-800AP) I previously mentioned. The other features/modes (Client, Bridge, ect) could come in handy, I suppose. (I have yet to use any of these features with the two DWL-7100AP's I recently got, but..) The DWL-2100AP, like the DWL-7100AP, also has an embedded DHCP server. That is something that I have used already beyond my home network. I took the DWL-7100AP over to a friend's house and using the DWL-7100AP in "AP Mode", which DHCP server enabled, we were able to quickly establish a WLAN for multiplayer gaming. Nice little extra feature that can come in handy. (The DWL-G800AP can also operate as a little AP, but doesn't have an embedded DHCP server. It would have been possible to use it to setup a quick WLAN for gaming as well, but everyone would've had to punched IP's into their tcp/ip properties for their wireless client hardware. DHCP just made it much more convienent.)
Run an ethernet cable from a LAN port on the second router to a LAN port on the first router. Disable DHCP on the second router. The DHCP from the first router will assign an IP address to the second router. As for the wireless feature, use the same SSID and encryption as with the first router, but place the second router on a different channel. This SHOULD provide you with the setup you seek.